Dissertations / Theses on the topic 'Riemannsk geometri'
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Pedersen, Morten Akhøj. "Méthodes riemanniennes et sous-riemanniennes pour la réduction de dimension." Electronic Thesis or Diss., Université Côte d'Azur, 2023. http://www.theses.fr/2023COAZ4087.
In this thesis, we propose new methods for dimension reduction based on differential geometry, that is, finding a representation of a set of observations in a space of lower dimension than the original data space. Methods for dimension reduction form a cornerstone of statistics, and thus have a very wide range of applications. For instance, a lower dimensional representation of a data set allows visualization and is often necessary for subsequent statistical analyses. In ordinary Euclidean statistics, the data belong to a vector space and the lower dimensional space might be a linear subspace or a non-linear submanifold approximating the observations. The study of such smooth manifolds, differential geometry, naturally plays an important role in this last case, or when the data space is itself a known manifold. Methods for analysing this type of data form the field of geometric statistics. In this setting, the approximating space found by dimension reduction is naturally a submanifold of the given manifold. The starting point of this thesis is geometric statistics for observations belonging to a known Riemannian manifold, but parts of our work form a contribution even in the case of data belonging to Euclidean space, mathbb{R}^d.An important example of manifold valued data is shapes, in our case discrete or continuous curves or surfaces. In evolutionary biology, researchers are interested in studying reasons for and implications of morphological differences between species. Shape is one way to formalize morphology. This application motivates the first main contribution of the thesis. We generalize a dimension reduction method used in evolutionary biology, phylogenetic principal component analysis (P-PCA), to work for data on a Riemannian manifold - so that it can be applied to shape data. P-PCA is a version of PCA for observations that are assumed to be leaf nodes of a phylogenetic tree. From a statistical point of view, the important property of such data is that the observations (leaf node values) are not necessarily independent. We define and estimate intrinsic weighted means and covariances on a manifold which takes the dependency of the observations into account. We then define phylogenetic PCA on a manifold to be the eigendecomposition of the weighted covariance in the tangent space of the weighted mean. We show that the mean estimator that is currently used in evolutionary biology for studying morphology corresponds to taking only a single step of our Riemannian gradient descent algorithm for the intrinsic mean, when the observations are represented in Kendall's shape space. Our second main contribution is a non-parametric method for dimension reduction that can be used for approximating a set of observations based on a very flexible class of submanifolds. This method is novel even in the case of Euclidean data. The method works by constructing a subbundle of the tangent bundle on the data manifold via local PCA. We call this subbundle the principal subbundle. We then observe that this subbundle induces a sub-Riemannian structure and we show that the resulting sub-Riemannian geodesics with respect to this structure stay close to the set of observations. Moreover, we show that sub-Riemannian geodesics starting from a given point locally generate a submanifold which is radially aligned with the estimated subbundle, even for non-integrable subbundles. Non-integrability is likely to occur when the subbundle is estimated from noisy data, and our method demonstrates that sub-Riemannian geometry is a natural framework for dealing which such problems. Numerical experiments illustrate the power of our framework by showing that we can achieve impressively large range reconstructions even in the presence of quite high levels of noise
I denne afhandling præsenteres nye metoder til dimensionsreduktion, baseret p˚adifferential geometri. Det vil sige metoder til at finde en repræsentation af et datasæti et rum af lavere dimension end det opringelige rum. S˚adanne metoder spiller enhelt central rolle i statistik, og har et meget bredt anvendelsesomr˚ade. En laveredimensionalrepræsentation af et datasæt tillader visualisering og er ofte nødvendigtfor efterfølgende statistisk analyse. I traditionel, Euklidisk statistik ligger observationernei et vektor rum, og det lavere-dimensionale rum kan være et lineært underrumeller en ikke-lineær undermangfoldighed som approksimerer observationerne.Studiet af s˚adanne glatte mangfoldigheder, differential geometri, spiller en vigtig rollei sidstnævnte tilfælde, eller hvis rummet hvori observationerne ligger i sig selv er enmangfoldighed. Metoder til at analysere observationer p˚a en mangfoldighed udgørfeltet geometrisk statistik. I denne kontekst er det approksimerende rum, fundetvia dimensionsreduktion, naturligt en submangfoldighed af den givne mangfoldighed.Udgangspunktet for denne afhandling er geometrisk statistik for observationer p˚a ena priori kendt Riemannsk mangfoldighed, men dele af vores arbejde udgør et bidragselv i tilfældet med observationer i Euklidisk rum, Rd.Et vigtigt eksempel p˚a data p˚a en mangfoldighed er former, i vores tilfældediskrete kurver eller overflader. I evolutionsbiologi er forskere interesseret i at studeregrunde til og implikationer af morfologiske forskelle mellem arter. Former er ´en m˚adeat formalisere morfologi p˚a. Denne anvendelse motiverer det første hovedbidrag idenne afhandling. We generaliserer en metode til dimensionsreduktion brugt i evolutionsbiologi,phylogenetisk principal component analysis (P-PCA), til at virke for datap˚a en Riemannsk mangfoldighed - s˚a den kan anvendes til observationer af former. PPCAer en version af PCA for observationer som antages at være de yderste knuder iet phylogenetisk træ. Fra et statistisk synspunkt er den vigtige egenskab ved s˚adanneobservationer at de ikke nødvendigvis er uafhængige. We definerer og estimerer intrinsiskevægtede middelværdier og kovarianser p˚a en mangfoldighed, som tager højde fors˚adanne observationers afhængighed. Vi definerer derefter phylogenetisk PCA p˚a enmangfoldighed som egendekomposition af den vægtede kovarians i tanget-rummet tilden vægtede middelværdi. Vi viser at estimatoren af middelværdien som pt. bruges ievolutionsbiologi til at studere morfologi svarer til at tage kun et enkelt skridt af voresRiemannske gradient descent algoritme for den intrinsiske middelværdi, n˚ar formernerepræsenteres i Kendall´s form-mangfoldighed.Vores andet hovedbidrag er en ikke-parametrisk metode til dimensionsreduktionsom kan bruges til at approksimere et data sæt baseret p˚a en meget flexibel klasse afsubmangfoldigheder. Denne metode er ny ogs˚a i tilfældet med Euklidisk data. Metodenvirker ved at konstruere et under-bundt af tangentbundet p˚a datamangfoldighedenM via lokale PCA´er. Vi kalder dette underbundt principal underbundtet. Viobserverer at dette underbundt inducerer en sub-Riemannsk struktur p˚a M og vi viserat sub-Riemannske geodæter fra et givent punkt lokalt genererer en submangfoldighedsom radialt flugter med det estimerede subbundt, selv for ikke-integrable subbundter.Ved støjfyldt data forekommer ikke-integrabilitet med stor sandsynlighed, og voresmetode demonstrerer at sub-Riemannsk geometri er en naturlig tilgang til at h˚andteredette. Numeriske eksperimenter illustrerer styrkerne ved metoden ved at vise at denopn˚ar rekonstruktioner over store afstande, selv under høje niveauer af støj
Silva, Junior Roberto Carlos Alvarenga da [UNESP]. "Teorema de Riemann-Roch, morfismos de Frobenius e a hipótese de Riemann." Universidade Estadual Paulista (UNESP), 2014. http://hdl.handle.net/11449/122107.
Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)
O objetivo desde trabalho e estimar um cota para o n umero de pontos racionais de uma curva. Observando as várias semelhanças entre o anel dos inteiros e o anel dos polinômios em uma variável, iremos usar ferramentas da teoria dos números para resolver um problema da geometria algébrica. Desta fusão nasce uma das mais nobres areas da matemática: a geometria aritmética. Fazendo uso do célebre teorema de Riemann-Roch e das ferramentas da teoria dos números demonstraremos a hipótese de Riemann para a funço-zeta de uma curva não singular e qual consequência tal hipótese tem para a contagem de pontos racionais de uma curva
The aim of this work is to estimate a bound for the number of rational points of a curve. Observing the various similarities between the ring of integers and the ring of polynomials in one variable, we use tools from number theory to solve a problem of algebraic geometry. From this merger is born one of the noblest areas of mathematics: arithmetic geometry. Making use of the famous Riemann-Roch's theorem and tools of number theory we demonstrate the Riemann hypothesis for the zeta-function of a nonsingular curve and which consequence this hypothesis has to count rational points on a curve
Silva, Junior Roberto Carlos Alvarenga da. "Teorema de Riemann-Roch, morfismos de Frobenius e a hipótese de Riemann /." São José do Rio Preto, 2014. http://hdl.handle.net/11449/122107.
Banca: Eduardo Tengan
Banca: Trajano Pires da Nóbrega Neto
Resumo: O objetivo desde trabalho e estimar um cota para o n umero de pontos racionais de uma curva. Observando as várias semelhanças entre o anel dos inteiros e o anel dos polinômios em uma variável, iremos usar ferramentas da teoria dos números para resolver um problema da geometria algébrica. Desta fusão nasce uma das mais nobres areas da matemática: a geometria aritmética. Fazendo uso do célebre teorema de Riemann-Roch e das ferramentas da teoria dos números demonstraremos a hipótese de Riemann para a funço-zeta de uma curva não singular e qual consequência tal hipótese tem para a contagem de pontos racionais de uma curva
Abstract: The aim of this work is to estimate a bound for the number of rational points of a curve. Observing the various similarities between the ring of integers and the ring of polynomials in one variable, we use tools from number theory to solve a problem of algebraic geometry. From this merger is born one of the noblest areas of mathematics: arithmetic geometry. Making use of the famous Riemann-Roch's theorem and tools of number theory we demonstrate the Riemann hypothesis for the zeta-function of a nonsingular curve and which consequence this hypothesis has to count rational points on a curve
Mestre
Silva, Lucio Fábio Pereira da. "Estruturas não-riemannianas e a imersão do espaço-tempo em dimensões superiores." Universidade Federal da Paraíba, 2012. http://tede.biblioteca.ufpb.br:8080/handle/tede/5732.
Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES
We consider the geometry of affine connections and take, as particular examples, Weyl and Riemann-Cartan geometies. In a modern geometrical approach, we take up the problem of local embedding of manifolds in Weyl spaces and in spaces endowed with semi-symmetric torsion. We then obtain the extrinsic curvature, Weingarten operator and Gauss-Codazzi equations in the mentioned non-riemannian spaces. We investigate some important properties of a Weyl structure in the case of a warped product and carry out an analysis of the geodesics in a foliation de…ned in such a space. We consider the particular case when the embedding space is a warped product manifold and has a Riemann-Cartan geometry. As an application, we show that the torsion …eld of de bulk may provide a mechanism of geometrical con…nement. In this way, we exhibit a classical analogue of the quantum con…nement induced by scalar …elds.
Consideramos a geometria de uma conexão a…m e abordamos como exemplos, as geometrias de Weyl e Riemann-Cartan, esta ultima considerando o caso em que a torção é semi-simétrica. Após uma exposição moderna das propriedades destas geometrias, abordamos o problema de imersões isométricas em espaços de Weyl e de torção semi-simétrica. Introduzimos um roteiro para a obtenção da curvatura extrínseca, operador de Weingarten e das equações de Gauss-Codazzi para tais espaços. Em seguida, analisamos as propriedades de uma estrutura de Weyl em um espaço produto distorcido (EPD) e analisamos as geodésicas das folhas em tal espaço. Consideramos, também, o caso particular quando o espaço ambiente para um (EPD) com uma geometria de Riemann-Cartan. Mostramos como o confi…namento e as propriedades de estabilidade de geodésicas próximas ao mundo-brana podem ser afetadas pela torção do bulk. Deste modo, construímos um análogo clássico do confi…namento quântico inspirado em modelos de teoria de campo, substituindo um campo escalar por um campo de torção.
Stavrov, Iva. "Spectral geometry of the Riemann curvature tensor /." view abstract or download file of text, 2003. http://wwwlib.umi.com/cr/uoregon/fullcit?p3095275.
Typescript. Includes vita and abstract. Includes bibliographical references (leaves 236-241). Also available for download via the World Wide Web; free to University of Oregon users.
Lopes, Lauriclecio Figueiredo. "Superficies minimas folheadas por circunferencias." [s.n.], 2005. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306661.
Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica
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Resumo: Entende-se por superfícies mínimas aquelas cuja curvatura média é nula. Têm-se como exemplos clássicos o catenóide, o helicóide e a superfície de Scherk. Historicamente, elas estão relacionadas com minimização de área, porém quando realiza-se uma variação normal incluindo os bordos, a superfície original com curvatura média nula pode representar uma área localmente máxima. Em certos casos de variação com bordo fixo, tem-se realmente a minimização do funcional área. No espaço euclidiano tridimensional, o Teorema da Representação de Weierstrass expressa uma superfície mínima em termos de integrais envolvendo uma função holomorfa e uma meromorfa. A partir desta meromorfa pode-se deduzir a aplicação normal de Gauss. Conceitos como curvatura Gaussiana, curvatura total, superfícies completas e regularidade também são utilizados para deduzir propriedades das superfícies mínimas. Quando estudamos as superfícies mínimas para as quais o bordo consiste de duas circunferências disjuntas, os Teoremas de Enneper e Shiffman, o Princípio de Reflexão de Schwarz e a unicidade do Problema de Bjõrling são ferramentas importantes para a dedução das soluções, a saber, o catenóide e as superfícies de Riemann. Estas apresentam simetrias por reflexão a um plano e invariância por rotação de 180 graus em torno de uma reta. A função "P de Weierstrass" simétrica é de grande utilidade no estudo destas propriedades
Abstract: Minimal surfaces are known to be the ones with mean curvature zero. Classical exampIes are the catenoid, helicoid and the Scherk surface. Historically, they were associated with the property of minimizing area. However, they can even maximize it localIy for cases of normal variation which include the boundary. For fixed boundary, we shalI analyse when they realIy minimize the area functional. In the three-dimensional Euclidean space, the Weierstrass Representation Theorem expresses any minimal surface S by means of integraIs with a holomorphic and a meromorphic functions, usualIy denoted by f and g, respectively. The unitary normal N of S is fulIy determined by g. Concepts like "Gaussian curvature", "total curvature", "com pleteness" and "regularity" are also employed in order to read off some properties of minimal surfaces. Concerning the case for which the boundary of S consists of two disjoint circumferences, Enneper's and Shiffman's Theorems, The Schwarz's Reflection PrincipIe and the B6rling's Problem are fundamental tools to characterize the solutions, namely the catenoid and the Riemann's examples. AlI these are invariant by a reflectional symmetry in a plane, and also by a rotation of 180-degree around a straight line. The symmetric Weierstrass-Pfunction is very useful to deduce these properties
Mestrado
Matematica
Mestre em Matemática
Lubeck, Kelly Roberta Mazzutti. "Metodo limite para solução de problemas de periodos em superficies minimas." [s.n.], 2007. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306660.
Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica
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Resumo: Neste trabalho apresentamos o estudo e a construção de superfícies minimas atraves de um metodo exclusivo. Em 1762, Lagrange introduziu a Equacao Diferencial das Superfícies Mnimas atraves do Calculo de Variações, e hoje a teoria de tais superfícies e umaarea de pesquisa ativa e abrangente. A elaboração de novas famílias de superfícies minimas esta baseada no metodo da Construção Reversa, desenvolvido por Hermann Karcher nos meados da década de 80. Salientamos no presente trabalho a maneira diferenciada com que os problemas de periodos foram resolvidos. Para isso, utilizaram-se as equações de uma superfície mínima limite, para a qual ja era conhecido que o problema de períodos tinha solução transversal. Tal método, que neste trabalho sera denominado "método limite", simplica de maneira consideravel o esforco em solucionar os problemas de período da família original
Abstract: In this work we present the study and construction of minimal surfaces through an exclusive method. In 1762, Lagrange introduced the Minimal Surfaces Diferential Equation through the Calculus of Variations, and today the theory of such surfaces builds up an active and broad research area. We obtain new families of minimal surfaces based upon the Reverse Construction Method, developed by Hermann Karcher during the eighties. In our work we stress the original fashion with which period problems are solved: One makes use of a limit minimal surface, of which the periods are known to have transversal solution. Because of that we named our technique as "limit-method", which simplies considerably the effort of solving period problems for the sought after family of minimal surfaces
Doutorado
Geometria Diferencial
Mestre em Matemática
Porto, Anderson Corrêa. "Divisores sobre curvas e o Teorema de Riemann-Roch." Universidade Federal de Juiz de Fora (UFJF), 2018. https://repositorio.ufjf.br/jspui/handle/ufjf/6612.
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O objetivo desse trabalho é o estudo de conceitos básicos da Geometria Algébrica sob o ponto de vista clássico. O foco central do trabalho é o estudo do Teorema de Riemann- Roch e algumas de suas aplicações. Esse teorema constitui uma importante ferramenta no estudo da Geometria Algébrica clássica uma vez que possibilita, por exemplo, o cáculo do gênero de uma curva projetiva não singular no espaço projetivo de dimensão dois. Para o desenvolvimento do estudo do Teorema de Riemann-Roch e suas aplicações serão estudados conceitos tais como: variedades, dimensão, diferenciais de Weil, divisores, divisores sobre curvas e o anel topológico Adèle.
The goal of this work is the study of basic concepts of Algebraic Geometry from the classical point of view. The central focus of the paper is the study of Riemann-Roch Theorem and some of its applications. This theorem constitutes an important tool in the study of classical Algebraic Geometry since it allows, for example, the calculation of the genus of a non-singular projective curve in the projective space of dimension two. For the development of the study of the Riemann-Roch Theorem and its applications we will study concepts such as: varieties, dimension, Weil differentials, divisors, divisors on curves and the Adèle topological ring.
Reyes, Ernesto Oscar. "The Riemann zeta function." CSUSB ScholarWorks, 2004. https://scholarworks.lib.csusb.edu/etd-project/2648.
Souici, Zobida. "Transformations holomorphiquement projectives des espaces symétriques complexes." Lyon 1, 1988. http://www.theses.fr/1988LYO11758.
Murri, Riccardo. "Computational techniques in graph homology of the moduli space of curves." Doctoral thesis, Scuola Normale Superiore, 2013. http://hdl.handle.net/11384/85723.
Jacyntho, Luiz Antonio. "Uso de episodios historicos e de geometria dinamica para desenvolvimento de coneitos de integral de Riemann e do teorema fundamental do calculo para funções reais de variavel real." [s.n.], 2008. http://repositorio.unicamp.br/jspui/handle/REPOSIP/305871.
Dissertação (mestrado profissional) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação
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Resumo: Este trabalho tem como objetivos estudar algumas realizações de Arquimedes (287 a.C. - 212 a.C., Grécia) e de Isaac Barrow (1630-1677, Inglaterra), e, também, desenvolver atividades no Geogebra para auxiliar no ensino do Cálculo Diferencial e Integral. Apresentamos a construção do conjunto dos números reais, definições e teoremas atuais que antecedem, logicamente, o Teorema Fundamental do Cálculo. Tratamos de algumas das realizações de Arquimedes: a demonstração da medida da área do círculo, utilizando o Método de Eudoxo, o "método mecânico", pelo qual ele descobriu a medida da área do segmento parabólico e a demonstração rigorosa desta medida. São discutidas algumas realizações de Isaac Barrow: o método por ele utilizado para encontrar retas tangentes a uma curva, um estudo sobre o conteúdo da Conferência I e sobre algumas proposições da Conferência X. Nesta última, será dada atenção especial à Proposição 11, que demonstra casos particulares do Teorema Fundamental do Cálculo. O trabalho termina com um conjunto de atividades baseadas no programa Geogebra. Cada atividade tem a sua função numa seqüência didática e aborda os seguintes temas: a representação do conjunto dos números reais, a proposição de Arquimedes sobre a medida da área do círculo, o cálculo de áreas, a construção da função área, o cálculo de primitivas, a interpretação de Barrow para casos particulares do Teorema fundamental do Cálculo e algumas aplicações do Teorema Fundamental do Cálculo
Abstract: This work has as objectives study some realizations of Archimedes (287 BC - 212 BC, Greece) and of Isaac Barrow (1630-1677, UK), and, also, develop activities in Geogebra to aid in the teaching of Differential and Integral Calculus. We present the construction of the set of the real numbers, definitions and actual theorems that precede, logically, the Fundamental Theorem of Calculus. We deal with some of Archimedes' realizations: the demonstration of the measure of the circle's area, using the Eudoxus' Method, the "mechanical method", by which he discovered the measure of the area of the parabolic segment and the rigorous demonstration of it. There are discussed some realizations of Isaac Barrow: the method used by him to find tangent straights to a curve, a study about the content of the Lecture I and about some prepositions of the Lecture X. In this last one, main attention will be given to Proposition 11, which demonstrates particular cases of the Fundamental Theorem of Calculus. The word ends with a group of activities based in the Geogebra. Each activity has its function in a didactic sequence and they are about the following themes: the representation of the set of the real numbers, the proposition of Archimedes about the measure of the area of the circle, the calculation of areas, the construction of the area function, the calculation of primitives, the interpretation of Barrow to particular cases of the Fundamental Theorem of Calculus and some applications of the Fundamental Theorem of Calculus
Mestrado
Geometria
Mestre em Matemática
Raiz, Caio Eduardo Martins. "Transformações de Mobius e projeções na esfera de Riemann." Universidade de São Paulo, 2018. http://www.teses.usp.br/teses/disponiveis/55/55136/tde-22032019-162007/.
In the course of this dissertation we explore the geometric effects of the Möbius Transforms in C using projections in the Riemann sphere. As an application, we present the action of some transformations applied on conics in the plane. A didactic activity aimed at high school students about Möbius Transformations using Geogebra is presented.
Pablo, MartiÌn GarciÌa. "Embedding of some finite geometries into Riemann surfaces." Thesis, University of Southampton, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.409755.
Wu, Bao Qiang. "Geometry of complete Riemannian Submanifolds." Lyon 1, 1998. http://www.theses.fr/1998LYO10064.
Rink, Norman Alexander. "Complex geometry of vortices and their moduli spaces." Thesis, University of Cambridge, 2013. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.607939.
Alves, Alessandro Ferreira. "Análise dos emparelhamentos de arestas de polígonos hiperbólicos para a construção de constelações de sinais geometricamente uniformes." [s.n.], 2011. http://repositorio.unicamp.br/jspui/handle/REPOSIP/261080.
Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Elétrica e de Computação
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Resumo: Para projetarmos um sistema de comunicação digital em espaços hiperbólicos é necessário estabelecer um procedimento sistemático de construção de reticulados como elemento base para a construção de constelações de sinais. De outra forma, em codificação de canal é de fundamental importância a caracterização das estruturas algébrica e geométrica associadas a canais discretos sem memória. Neste trabalho, apresentamos a caracterização geométrica de superfícies a partir dos possíveis emparelhamentos das arestas do polígono fundamental hiperbólico com 3 ? n ? 8 lados associado 'a superfície. Esse tratamento geométrico apresenta propriedades importantes na determinação dos reticulados hiperbólicos a serem utilizados no processo de construção de constelações de sinais, a partir de grupos fuchsianos aritméticos e da superfície de Riemann associada. Além disso, apresentamos como exemplo o desenvolvimento algébrico para a determinação dos geradores do grupo fuchsiano 'gama'8 associado ao polígono hiperbólico 'P IND. 8'
Abstract: In order to design a digital communication system in hyperbolic spaces is necessary to establish a systematic procedure of constructing lattices as the basic element for the construction of the signal constellations. On the other hand, in channel coding is of fundamental importance to characterize the geometric and algebraic structures associated with discrete memoryless channels. In this work, we present a geometric characterization of surfaces from the edges of the possible pairings of fundamental hyperbolic polygon with 3 ? n ? 8 sides associated with the surface. This treatment has geometric properties important in determining the hyperbolic lattices to be used in the construction of sets of signals derived from arithmetic Fuchsian groups and the associated Riemann surface
Doutorado
Telecomunicações e Telemática
Doutor em Engenharia Elétrica
Zanon, Denise Elena Fagan. "Três métodos para o cálculo da série zeta(2n) de Riemann." reponame:Biblioteca Digital de Teses e Dissertações da UFRGS, 2006. http://hdl.handle.net/10183/6838.
Gaslowitz, Joshua Z. "Chip Firing Games and Riemann-Roch Properties for Directed Graphs." Scholarship @ Claremont, 2013. http://scholarship.claremont.edu/hmc_theses/42.
Subiabre, Sánchez Felipe Ignacio. "Fenómenos de concentración en geometría y análisis no lineal." Tesis, Universidad de Chile, 2014. http://www.repositorio.uchile.cl/handle/2250/116846.
El trabajo presentado en esta memoria se sitúa en la interfaz entre el análisis y la geometría. El interés recae en el estudio de fenómenos de concentración para dos problemas "geométricos" no lineales: la existencia de hipersuperficies con r-curvatura constante en variedades Riemannianas, y una ecuación de Schrödinger no lineal. Esta memoria se puede dividir en dos partes principales. La primera está dedicada a explorar algunos resultados sobre concentración de familias de hipersuperficies de curvatura media constante (o en general curvatura r-media constante) con topología no trivial en variedades Riemannianas compactas. Se recuerda que la curvatura r-media de una hipersuperficie se define como la r-ésima función simétrica elemental de las curvaturas principales de la hipersuperficie. Se prueba que las técnicas desarrolladas en el trabajo de Mahmoudi, Mazzeo y Pacard se pueden extender para manejar el caso de curvatura r-media con r>=1. Este fenómeno de concentración se relaciona en general con un fenómeno de resonancia, que hace el análisis particularmente delicado y que también se encuentra en el estudio de una clase de ecuaciones elípticas no lineales que presentan concentración sobre conjuntos de dimensión mayor. En la segunda parte, correspondiente al paper presentado, se prueba un nuevo resultado sobre concentración en subvariedades para una ecuación de Schrödinger no lineal con potencial definido en una variedad Riemanniana suave y compacta M o el espacio Euclídeo R^n, resolviendo en completa generalidad una conjetura planteada por Ambrosetti, Malchiodi y Ni. Precisamente, se estudian soluciones positivas de la siguiente ecuación semilineal: $$\e^2\Delta_{\bar g} u - V(z)u + u^{p} =0 en M,$$ donde (M,g) es una variedad Riemanniana n-dimensional suave, compacta y sin borde o el espacio Euclídeo R^n, e es un parámetro positivo pequeño, p>1 y V es un potencial uniformemente positivo. Se prueba que dado k=1,...,n-1 y 1
Turaça, Angélica. "As coordenadas de Fenchel-Nielsen." Universidade de São Paulo, 2015. http://www.teses.usp.br/teses/disponiveis/45/45132/tde-27082015-073617/.
In this dissertation, we defined the hyperbolic geometry using the Poincares disk (D2) and upper half-plane (H2) with its properties. Besides, we presented some functions and important relations of the hyperbolic geometry; we conceptualize the Riemann surfaces, analyzing its properties and representations; we studied the Teichmüller Space with proper decomposition pants. These themes are essential tools to reach the goal of the work: The definition of the Fenchel Nielsen coordenates as local coordinate system of the Teichmüller space Tg.
Usatine, Jeremy. "Arithmetical Graphs, Riemann-Roch Structure for Lattices, and the Frobenius Number Problem." Scholarship @ Claremont, 2014. http://scholarship.claremont.edu/hmc_theses/57.
Bastos, Jefferson Luiz Rocha. "Forma combinada de conjunto de sinais e codigos de Goppa atraves da geometria algebrica." [s.n.], 2007. http://repositorio.unicamp.br/jspui/handle/REPOSIP/261299.
Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Eletrica e de Computação
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Resumo: Tendo como base trabalhos recentes que associam o desempenho de sistemas de comunicação digital ao gênero de uma superfície compacta de Riemann, este trabalho tem como objetivo propor uma integração entre modulação e codificação de canal, tendo como base o gênero da superfície. Para atingir tais objetivos, nossa proposta é a seguinte: fixado um gênero g (g = 0,1,2,3), encontrar curvas com este gênero e fazer uma análise dos parâmetros dos códigos associados a esta curva, a fim de se obter uma modulação e um sub-código desta modulação para ser utilizado na codificação de canal
Abstract: Based on recent research showing that the performance of bandwidth efficent communication systems also depends on the genus of a. compact Riemann surface in which the communication channel is embedded, this study aims at proposing a combined form of modulation and coding technique when only the genus of a surface is given to the communication system designeI. To achieve this goal, the following procedure is proposed. Knowing that the channel is embedded in a surface of genus g, find algebraic curves with the given genus which will give rise to the modulation system, an (n, n, 1) type of code, and from this find the best (n, k, d) subcode, to be employed in the aforementioned combined formo Keywords: Riemann surface, algebraic curves, Goppa codes, modulation
Doutorado
Engenharia de Computação
Doutor em Engenharia Elétrica
Escudero, Salcedo Carlos Arturo. "Conjuntos focales en variedades de Riemann de curvatura acotada." Doctoral thesis, Universitat Autònoma de Barcelona, 2006. http://hdl.handle.net/10803/3096.
Correia, Nuno Miguel Ferreira. "Aplicações harmónicas de superfícies de Riemann sobre espaços simétricos." Doctoral thesis, Universidade da Beira Interior, 2012. http://hdl.handle.net/10400.6/1877.
Bartolini, Gabriel. "On Poicarés Uniformization Theorem." Thesis, Linköping University, Department of Mathematics, 2006. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-7968.
A compact Riemann surface can be realized as a quotient space $\mathcal{U}/\Gamma$, where $\mathcal{U}$ is the sphere $\Sigma$, the euclidian plane $\mathbb{C}$ or the hyperbolic plane $\mathcal{H}$ and $\Gamma$ is a discrete group of automorphisms. This induces a covering $p:\mathcal{U}\rightarrow\mathcal{U}/\Gamma$.
For each $\Gamma$ acting on $\mathcal{H}$ we have a polygon $P$ such that $\mathcal{H}$ is tesselated by $P$ under the actions of the elements of $\Gamma$. On the other hand if $P$ is a hyperbolic polygon with a side pairing satisfying certain conditions, then the group $\Gamma$ generated by the side pairing is discrete and $P$ tesselates $\mathcal{H}$ under $\Gamma$.
Silva, Cleusiane Vieira da. "Aplicações harmonicas, estruturas-f, toros e superficies de Riemann nas variedades homogeneas." [s.n.], 2002. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306781.
Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica
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Resumo: Neste trabalho, estudamos a geometria das estruturas-f invariantes e curvas fholomorfas em variedades bandeira, a construção de toros equiharmônicos em variedades bandeira complexas não-degeneradas que não são f-holomorfos para qualquer estrutura-f invariante. Calculamos a segunda variação da energia para superfícies harmônicas riemannianas fechadas em variedades bandeira munidas com métricas do tipo Borel daídiscutimos a estabilidade para o referencial de Frenet de aplicações holomorfas com respeito a uma grande classe de métricas invariantes em F(N) obtidas via perturbação de métricas Kãhler. Além disso relacionamos a teoria de torneios com as estruturas quase complexas de uma variedade bandeira. Finalmente mostramos que a métrica Killing em F(N) é (1,2)-simplética se e somente se N :S 3
Abstract: In this work we study the geometry of invariant f-structures and f-holomorphic curves on flag manifolds, and the construction of the equiharmonic tori on full complex flag manifolds which are not f-holomophic for any invariant f-estructure. Moreover we relate the tournament theory with the almost-complex on a flag manifolds. We compute the second variation of energy for harmonic closed Riemann surfaces into flag manifolds equipped with the Borel type metrics then we discuss stability for Frenet frames of holomorphics maps with respect to a very large class de invariants metrics F(N) obtained via perturbation of the Kãhler ones. Finally we proof that the metric Killing on F(N) is (1,2)-simplétic if and only if N :S 3
Mestrado
Mestre em Matemática
Sumi, Ken. "Tropical Theta Functions and Riemann-Roch Inequality for Tropical Abelian Surfaces." Doctoral thesis, Kyoto University, 2021. http://hdl.handle.net/2433/263432.
Patria, Francesca. "La sfera tra cartografia e geometrie non euclidee." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2018. http://amslaurea.unibo.it/17076/.
Clarenz, Ulrich. "Sätze über Extremalen zu parametrischen Funktionalen." Bonn : [Mathematisches Institut der Universität Bonn], 1999. http://catalog.hathitrust.org/api/volumes/oclc/45517656.html.
Costa, Maria de Andrade. "O teorema de H. Hopf e as inequações de Cauchy-Riemann." Universidade Federal de Alagoas, 2006. http://repositorio.ufal.br/handle/riufal/1049.
Em 1951, H. Hopf publicou em um prestigiado artigo um famoso resultado: Seja M uma superfície compacta de gênero zero imersa no espaço Euclidiano de dimensão três com curvatura média constante. Então M é isométrica à esfera redonda. Neste trabalho descreveremos detalhadamente do ponto de vista matemático uma generalização do resultado obtido por H. Hopf, a qual será publicada na revista Communication in Analysis and Geometry em 2007, cujos autores são Hilário Alencar, Manfredo Perdigão do Carmo e Renato Tribuzy. Neste artigo, os pesquisadores classificaram as superfíıcies compactas de gênero zero imersas na variedade produto: superfícies com curvatura Gaussiana constante cartesiano o espaço Euclidiano de dimensão um e cuja diferencial da curvatura média satisfaz uma certa desigualdade envolvendo uma forma quadrátrica. Além disso, estudaremos uma extensão da classificação anterior no caso em que as superfícies estão imersas numa variedade Riemanniana simplesmente conexa, homogênea com um grupo de isometrias de dimensão quatro. Tais resultados foram obtidos recentemente por Hilário Alencar, Isabel Fernández, Manfredo Perdigão do Carmo e Renato Tribuzy. Nas demonstrações destes teoremas foram usadas técnicas de Análise Complexa, fatos de Topologia e uma generalização do Teorema de H. Hopf obtida por Abresch e Rosenberg, publicado em Acta Mathematica em 2004.
Cook, Joseph. "Properties of eigenvalues on Riemann surfaces with large symmetry groups." Thesis, Loughborough University, 2018. https://dspace.lboro.ac.uk/2134/36294.
Arruda, Rafael Lucas de [UNESP]. "Teorema de Riemann-Roch e aplicações." Universidade Estadual Paulista (UNESP), 2011. http://hdl.handle.net/11449/86493.
Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)
O objetivo principal deste trabalho é estudar o Teorema de Riemann-Roch, um dos resultados fundamentais na teoria de curvas algébricas, e apresentar algumas de suas aplicações. Este teorema é uma importante ferramenta para a classificação das curvas algébricas, pois relaciona propriedades algébricas e topológicas. Daremos uma descrição das curvas algébricas de gênero g, 1≤ g ≤ 5, e faremos um breve estudo dos pontos de inflexão de um sistema linear sobre uma curva algébrica
The main purpose of this work is to discuss The Riemann-Roch Theorem, wich is one of the most important results of the theory algebraic curves, and to present some applications. This theorem is an important tool of the classification of algebraic curves, sinces relates algebraic and topological properties. We will describle the algebraic curves of genus g, 1≤ g ≤ 5, and also study inflection points of a linear system on an algebraic curve
Rossi, Francesco. "Sub-Riemannian geometry and hypoelliptic heat equations on 3D Lie groups with applications to image reconstruction." Dijon, 2009. http://www.theses.fr/2009DIJOS029.
This thesis focuses on problems of sub-Riemannian geometry and on the corresponding subelliptic diffusion equation. These studies are motivated by a model of visual perception due to Petitot-Citti-Sarti. We study the invariant Carnot--Caratheodory metrics on SU(2)=S^3, SO(3), and SL(2). We compute the cut loci globally and the distance. This is the first explicit computation of the whole cut locus in sub-Riemannian geometry, except for the Heisenberg group. We present a definition of the hypoelliptic Laplacian that generalizes the Laplace-Beltrami operator. We present a method to compute explicitly the hypoelliptic heat kernels on Lie groups. The main tool is the noncommutative Fourier transform. We study some relevant cases: SU(2), SO(3), SL(2) and the group of rototranslations of the plane. We study the model of visual perception by PCS, for which the reconstruction of a corrupted curve \gamma is the minimization of a cost depending on length and curvature K. We fix starting and ending points as well as initial and final directions. We prove the non-existence of minimizers for \int \sqrt{1+K_\gamma^2} ds. We instead prove existence of minimizers for J=\int \| \dot\gamma(t) \|\sqrt{1+K_\gamma^2} dt if initial and final directions are considered regardless to orientation. We solve globally the problem of minimization of J on the sphere S^2. Some optimal geodesics present cusps. We present an algorithm of image reconstruction based on the model, where the minimization process is replaced by an hypoelliptic heat diffusion, that we solve explicitly. Examples of image reconstruction are provided
Marhenke, Jörg. "On algorithms for coding and decoding algebraic-geometric codes and their implementation." [S.l. : s.n.], 2008. http://nbn-resolving.de/urn:nbn:de:bsz:289-vts-65822.
Lenglet, Christophe. "Geometric and variational methods for diffusion tensor MRI processing." Nice, 2006. http://www.theses.fr/2006NICE4083.
This thesis deals with the development of new processing tools for Diffusion Tensor Magnetic Resonance Imaging (DT-MRI). This recent MRI technique is of utmost importance to acquire a better understanding of the brain mechanisms and to improve the diagnosis of neurological disorders. We introduce new algorithms relying on Riemannian geometry, partial differential equations and front propagation techniques. The first part of this work is theoretical. After a few reminders about the human nervous system, MRI and differential geometry, we study the space of multivariate normal distributions. The introduction of a Riemannian structure on that space allows us to define statistics and intrinsic numerical schemes that will constitute the core of the algorithms proposed in the second part. The properties of that space are important for DT-MRI since diffusion tensors are the covariance matrices of normal laws modeling the diffusion of water molecules at each voxel of the acquired volume. The second part of this thesis is methodological. We start with the introduction of original approaches for the estimation and regularization of DT-MRI. We then show how to evaluate the degree of connectivity between cortical areas. Next, we introduce a statistical surface evolution framework for the segmentation of those images. Finally, we propose a non-rigid registration method. The last part of this thesis is dedicated to the application of our tools to two important neuroscience problems: the analysis of the connections between the cerebral cortex and the basal ganglia, implicated in motor tasks, and the study of the anatomo-functional network of the human visual cortex
Hochard, Raphaël. "Théorèmes d’existence en temps court du flot de Ricci pour des variétés non-complètes, non-éffondrées, à courbure minorée." Thesis, Bordeaux, 2019. http://www.theses.fr/2019BORD0006/document.
The Ricci Flow is a partial differential equation governing the evolution of a Riemannian metric depending on a time parameter t on a differential manifold. It was first introduced and studied by R. Hamilton, and eventually led to the solution of the Geometrization conjecture for closed three-dimensional manifolds by G. Perelman in 2001. The classical short-time existence theory for the Ricci Flow, due to Hamilton and Shi, asserts, in any dimension, the existence of a flow starting from any initial metric when the underlying manifold in compact, or for any complete initial metric with a bound on the norm of the curvature tensor otherwise. In the absence of such a bound, though, the conjecture is that starting from dimension 3 one can find such initial data for which there is no solution. In this thesis, we prove short-time existence theorems under hypotheses weaker than a bound on the norm of the curvature tensor. To do this, we introduce a general construction which, for any Riemannian metric g (not necessarily complete) on a manifold M, allows us to produce a solution to the equation of the flow on an open domain D of the space-time M * [0,T] which contains the initial time slice, with g as an initial datum. We proceed to show that under suitable hypotheses on g, one can control the shape of the domain D, so that in particular, D contains a subset of the form M * [0,t] with t>0 if g is complete. By « suitable hypothesis », we mean one of the following. In any case, we assume a lower bound on the volume of balls of radius at most 1, plus a) in dimension 3, a lower bound on the Ricci tensor, b) in dimension n, a lower bound on the so-called « isotropic curvature I » or c) in dimension n, a bound on the norm of the Ricci tensor, as well as a hypothesis which garanties the metric proximity of every ball of radius at most $1$ with a ball of the same radius in a metric product between a three-dimensional metric space and a $n-3$ dimensional Euclidian factor. Moreover, with these existence results come estimates on the existence time and regularization properties of the flow, quantified in term of the hypotheses on the initial data. The possibility to regularize metrics, locally or globally, with such estimates has consequences in terms of the metric spaces obtained as limits, in the Gromov-Hausdorff topology, of sequences of manifolds uniformly satisfying a), b) or c). Indeed, the classical compactness theorems for the Ricci Flow allow for the extraction of a limit flow for any sequence of initial metrics uniformly satisfying the hypotheses and thus possessing a flow for a controlled amount of time. In the case when these metrics approach a singular space in the Gromov-Hausdorff topology, such a limit solution can be interpreted as a flow regularizing the singular limit space, the existence of which puts constraints on the topology of this space
Kacem, Anis. "Novel geometric tools for human behavior understanding." Thesis, Lille 1, 2018. http://www.theses.fr/2018LIL1I076/document.
Developing intelligent systems dedicated to human behavior understanding has been a very hot research topic in the few recent decades. Indeed, it is crucial to understand the human behavior in order to make machines able to interact with, assist, and help humans in their daily life.. Recent breakthroughs in computer vision and machine learning have made this possible. For instance, human-related computer vision problems can be approached by first detecting and tracking 2D or 3D landmark points from visual data. Two relevant examples of this are given by the facial landmarks detected on the human face and the skeletons tracked along videos of human bodies. These techniques generate temporal sequences of landmark configurations, which exhibit several distortions in their analysis, especially in uncontrolled environments, due to view variations, inaccurate detection and tracking, missing data, etc. In this thesis, we propose two novel space-time representations of human landmark sequences along with suitable computational tools for human behavior understanding. Firstly, we propose a representation based on trajectories of Gram matrices of human landmarks. Gram matrices are positive semi-definite matrices of fixed rank and lie on a nonlinear manifold where standard computational and machine learning techniques could not be applied in a straightforward way. To overcome this issue, we make use of some notions of the Riemannian geometry and derive suitable computational tools for analyzing Gram trajectories. We evaluate the proposed approach in several human related applications involving 2D and 3D landmarks of human faces and bodies such us emotion recognition from facial expression and body movements and also action recognition from skeletons. Secondly, we propose another representation based on the barycentric coordinates of 2D facial landmarks. While being related to the Gram trajectory representation and robust to view variations, the barycentric representation allows to directly work with standard computational tools. The evaluation of this second approach is conducted on two face analysis tasks namely, facial expression recognition and depression severity level assessment. The obtained results with the two proposed approaches on real benchmarks are competitive with respect to recent state-of-the-art methods
Ghazouani, Selim. "Structures affines complexes sur les surfaces de Riemann." Thesis, Paris Sciences et Lettres (ComUE), 2017. http://www.theses.fr/2017PSLEE022/document.
This thesis deals with several aspects of branched, complex affine structures on Riemann surfaces.In a first chapter, we study an algebraic invariant of these structures called holonomy, which is a representation of the fundamental group of the underlying surface into the affine group. We prove a theorem characterising such representations that arise as the holonomy of an affine structure.In a second part, we study certain moduli spaces of affine tori which happen to have an additional complex hyperbolic structure. We analyse the geometry of this structures in terms of degenerations of the underlying affine tori.Finally, we narrow our interest to a subclass of affine structures each element of which inducing a family of foliations on the underlying topological surface. We link these foliations to 1-dimensional dynamical systems called affine interval exchange transformations and study a particular case in details
Welliaveetil, John. "A study of skeleta in non-Archimedean geometry." Thesis, Paris 6, 2015. http://www.theses.fr/2015PA066162/document.
This thesis is a reflection of the interaction between Berkovich geometry and model theory. Using the results of Hrushovski and Loeser, we show that several interesting topological phenomena that concern the analytifications of varieties are governed by certain finite simplicial complexes embedded in them. Our work consists of the following two sets of results. Let k be an algebraically closed non-Archimedean non trivially real valued field which is complete with respect to its valuation. 1) Let $\phi : C' \to C$ be a finite morphism between smooth projective irreducible $k$-curves.The morphism $\phi$ induces a morphism $\phi^{an} : C'^{an} \to C^{an}$ between the Berkovich analytifications of the curves. We construct a pair of deformation retractions of $C'^{an}$ and $C^{an}$ which are compatible with the morphism $\phi^{\mathrm{an}}$ andwhose images $\Upsilon_{C'^{an}}$, $\Upsilon_{C^{an}}$ are closed subspaces of $C'^{an}$, $C^{an}$ that are homeomorphic to finite metric graphs. We refer to such closed subspaces as skeleta.In addition, the subspaces $\Upsilon_{C'^{an}}$ and $\Upsilon_{C^{an}}$ are such that their complements in their respective analytifications decompose into the disjoint union of isomorphic copies of Berkovich open balls. The skeleta can be seen as the union of vertices and edges, thus allowing us to define their genus. The genus of a skeleton in a curve $C$ is in fact an invariant of the curve which we call $g^{an}(C)$. The pair of compatible deformation retractions forces the morphism $\phi^{an}$ to restrict to a map $\Upsilon_{C'^{an}} \to \Upsilon_{C^{an}}$. We study how the genus of $\Upsilon_{C'^{an}}$ can be calculated using the morphism $\phi^{an}_{|\Upsilon_{C'^{an}}$ and invariants defined on $\Upsilon_{C^{an}}$. 2) Let $\phi$ be a finite endomorphism of $\mathbb{P}^1_k$. Given a closed point $x \in \mathbb{P}^1_k$, we are interested in the radius $f(x)$ of the largest Berkovich open ball centered at $x$ over which the morphism $\phi^{\mathrm{an}}$ is a topological fibration. Interestingly, the function $f : \mathbb{P}_k^1(k) \to \mathbb{R}_{\geq 0}$ admits a strong tameness property in that it is controlled by a non-empty finite graph contained in $\mathbb{P}^{1,an}_k$. We show that this result can be generalized to the case of finite morphisms $\phi : V' \to V$ between integral projective $k$-varieties where $V$ is normal
Arruda, Rafael Lucas de. "Teorema de Riemann-Roch e aplicações /." São José do Rio Preto : [s.n.], 2011. http://hdl.handle.net/11449/86493.
Banca: Eduardo de Sequeira Esteves
Banca: Jéfferson Luiz Rocha Bastos
Resumo: O objetivo principal deste trabalho é estudar o Teorema de Riemann-Roch, um dos resultados fundamentais na teoria de curvas algébricas, e apresentar algumas de suas aplicações. Este teorema é uma importante ferramenta para a classificação das curvas algébricas, pois relaciona propriedades algébricas e topológicas. Daremos uma descrição das curvas algébricas de gênero g, 1≤ g ≤ 5, e faremos um breve estudo dos pontos de inflexão de um sistema linear sobre uma curva algébrica
Abstract: The main purpose of this work is to discuss The Riemann-Roch Theorem, wich is one of the most important results of the theory algebraic curves, and to present some applications. This theorem is an important tool of the classification of algebraic curves, sinces relates algebraic and topological properties. We will describle the algebraic curves of genus g, 1≤ g ≤ 5, and also study inflection points of a linear system on an algebraic curve
Mestre
Ballón, Bordo Álvaro José. "Estructuras métricas de contacto y polinomios de Brieskorn-Pham." Master's thesis, Pontificia Universidad Católica del Perú, 2016. http://tesis.pucp.edu.pe/repositorio/handle/123456789/7486.
Tesis
Duma, Bertrand. "Vers la forme générale du théorème de Grothendieck-Riemann-Roch." Phd thesis, Université Paris-Diderot - Paris VII, 2012. http://tel.archives-ouvertes.fr/tel-00741782.
Rodado, A. Armando J. "Weierstrass points and canonical cell decompositions of the moduli and teichmüller spaces of riemann surfaces of genus two /." Connect to thesis, 2007. http://eprints.unimelb.edu.au/archive/00003539.
Figueroa, Serrudo Christian Bernardo. "Grupos de transformaciones en la geometría riemanniana." Pontificia Universidad Católica del Perú, 2014. http://repositorio.pucp.edu.pe/index/handle/123456789/95365.
Gomez, Gomez Jhon Elver. "Superficies de curvatura media constante en el espacio de Minkowski." Master's thesis, Pontificia Universidad Católica del Perú, 2019. http://hdl.handle.net/20.500.12404/15628.
Tesis
Xia, Baiqiang. "Learning 3D geometric features for soft-biometrics recognition." Thesis, Lille 1, 2014. http://www.theses.fr/2014LIL10132/document.
Soft-Biometric (gender, age, etc.) recognition has shown growingapplications in different domains. Previous 2D face based studies aresensitive to illumination and pose changes, and insufficient to representthe facial morphology. To overcome these problems, this thesis employsthe 3D face in Soft-Biometric recognition. Based on a Riemannian shapeanalysis of facial radial curves, four types of Dense Scalar Field (DSF) featuresare proposed, which represent the Averageness, the Symmetry, theglobal Spatiality and the local Gradient of 3D face. Experiments with RandomForest on the 3D FRGCv2 dataset demonstrate the effectiveness ofthe proposed features in Soft-Biometric recognition. Furtherly, we demonstratethe correlations of Soft-Biometrics are useful in the recognition. Tothe best of our knowledge, this is the first work which studies age estimation,and the correlations of Soft-Biometrics, using 3D face
Crétois, Rémi. "Automorphismes réels d'un fibré, opérateurs de Cauchy-Riemann et orientabilité d'espaces de modules." Phd thesis, Université Claude Bernard - Lyon I, 2011. http://tel.archives-ouvertes.fr/tel-00656631.
Hancco, Alvaro Julio Yucra. "Funções elíticas simétricas e aplicações em superfícies mínimas." Universidade Federal de São Carlos, 2010. https://repositorio.ufscar.br/handle/ufscar/5870.
Financiadora de Estudos e Projetos
In 1989, H.Karcher elaborated a method for the construction of minimal surfaces, denominated reverse construction method given in [10]. In that work it was rewritten the theory of elliptic functions using an approach more geometrical than analytical. This allows to better control the behavior and the image values of those functions, making it easier his application in minimal surfaces. In this master s thesis, we will present basic tools of the theory of symmetric elliptic functions, describing explicitly the symmetric ℘-Weierstraß and the function γ, that will be applied in the reverse construction method for an example of minimal surface.
Em 1989, H.Karcher elaborou um método para a construção de superfícies mínimas, denominada método de construção reversa dado em [10]. Nesse trabalho foi reescrita a teoria de funções elíticas utilizando uma abordagem mais geométrica do que analítica. Desse modo, ele conseguiu controlar o comportamento e os valores imagens dessas funções, facilitando sua aplicação em superfícies mínimas. Neste trabalho de mestrado, apresentamos ferramentas básicas da teoria de funções elíticas simétricas, descrevendo explicitamente a ℘-Weierstraß simétrica e a função γ, que serão aplicadas no método de construção reversa para um exemplo de superfície mínima.
Lope, Vicente Joe Moises. "Curvatura y fibrados principales sobre el círculo (Curvature and principal S 1 -bundles)." Master's thesis, Pontificia Universidad Católica del Perú, 2018. http://tesis.pucp.edu.pe/repositorio/handle/123456789/12829.
Tesis