Dissertations / Theses on the topic 'Pseudo-Riemannian manifolds'
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Dunn, Corey. "Curvature homogeneous pseudo-Riemannian manifolds /." view abstract or download file of text, 2006. http://proquest.umi.com/pqdweb?did=1188874491&sid=3&Fmt=2&clientId=11238&RQT=309&VName=PQD.
Full textTypescript. Includes vita and abstract. Includes bibliographical references (leaves 146-147). Also available for download via the World Wide Web; free to University of Oregon users.
Catalano, Domenico Antonino. "Concircular diffeomorphisms of pseudo-Riemannian manifolds /." [S.l.] : [s.n.], 1999. http://e-collection.ethbib.ethz.ch/show?type=diss&nr=13064.
Full textFriswell, Robert Michael. "Harmonic vector fields on pseudo-Riemannian manifolds." Thesis, University of York, 2014. http://etheses.whiterose.ac.uk/7878/.
Full textBotros, Amir A. "GEODESICS IN LORENTZIAN MANIFOLDS." CSUSB ScholarWorks, 2016. https://scholarworks.lib.csusb.edu/etd/275.
Full textGlobke, Wolfgang [Verfasser], and O. [Akademischer Betreuer] Baues. "Holonomy Groups of Flat Pseudo-Riemannian Homogeneous Manifolds / Wolfgang Globke. Betreuer: O. Baues." Karlsruhe : KIT-Bibliothek, 2011. http://d-nb.info/1014279771/34.
Full textTsonev, Dragomir. "Realisation of holonomy algebras on pseudo-Riemannian manifolds by means of Manakov operators." Thesis, Loughborough University, 2013. https://dspace.lboro.ac.uk/2134/12465.
Full textLischewski, Andree. "Geometric constructions and structures associated with twistor spinors on pseudo-Riemannian conformal manifolds." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät, 2015. http://dx.doi.org/10.18452/17132.
Full textThe present thesis studies local geometries admitting twistor spinors on pseudo- Riemannian manifolds of arbitrary signature. To this end, we refine and extend the necessary machinery of first prolongation of conformal structures and conformal tractor calculus which allows a conformally-invariant description of twistor spinors as parallel objects. In this context, our first main theorem is a classification result for conformal geometries whose conformal holonomy group admits a totally degenerate invariant subspace of arbitrary dimension. Based on this we are able to prove a partial classification result for conformal structures admitting twistor spinors. Moreover, we study the zero set of a twistor spinor using the theory of curved orbit decompositions for parabolic geometries. We can completely describe the local geometric structure of the zero set and show that locally every twistor spinor with zero is equivalent to a parallel spinor off the zero set. An application of these results in low-dimensional split-signatures leads to a complete geometric description of manifolds admitting non-generic twistor spinors in signatures (3,2) and (3,3) in terms of parallel spinors which complements the well-known analysis of the generic case. Moreover, we apply tractor calculus for the construction of a conformal superalgebra naturally associated to a conformal spin structure. This approach leads to various results linking algebraic properties of the superalgebra to special geometric structures on the underlying manifold. It also exhibits new construction principles for twistor spinors and conformal Killing forms. Finally, we introduce and elaborate on the notion of conformal Spin-c-geometry. Among other aspects, this gives rise to a new characterization of Fefferman spaces in terms of distinguished Spin-c-twistor spinors.
Lärz, Kordian. "Global aspects of holonomy in pseudo-Riemannian geometry." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, 2011. http://dx.doi.org/10.18452/16363.
Full textIn this thesis we study the interaction of holonomy and the global geometry of Lorentzian manifolds and pseudo-Riemannian submanifolds in spaces of constant curvature. In particular, we construct weakly irreducible, reducible Lorentzian metrics on the total spaces of certain circle bundles leading to a construction of Lorentzian manifolds with specified holonomy representations. Then we introduce a Bochner technique for Lorentzian manifolds admitting a nowhere vanishing parallel lightlike vector field whose orthogonal distribution has compact leaves. Finally, we classify normal holonomy representations of spacelike submanifolds in spaces of constant curvature and extend the classification to more general submanifolds.
Fama, Christopher J., and -. "Non-smooth differential geometry of pseudo-Riemannian manifolds: Boundary and geodesic structure of gravitational wave space-times in mathematical relativity." The Australian National University. School of Mathematical Sciences, 1998. http://thesis.anu.edu.au./public/adt-ANU20010907.161849.
Full textLischewski, Andree [Verfasser], Helga [Akademischer Betreuer] Baum, Hans Bert [Akademischer Betreuer] Rademacher, and José [Akademischer Betreuer] Figueroa-O'Farrill. "Geometric constructions and structures associated with twistor spinors on pseudo-Riemannian conformal manifolds / Andree Lischewski. Gutachter: Helga Baum ; Hans Bert Rademacher ; José Figueroa-O'Farrill." Berlin : Mathematisch-Naturwissenschaftliche Fakultät, 2015. http://d-nb.info/1067484841/34.
Full textTholozan, Nicolas. "Uniformisation des variétés pseudo-riemanniennes localement homogènes." Thesis, Nice, 2014. http://www.theses.fr/2014NICE4079/document.
Full textIn this work, we study closed locally homogeneous pseudo-Riemannian manifolds through the notion of (G,X)-structure, introduced by Thurston in his geometrization program. We start by presenting the general problem. In particular, we discuss the link between geodesical completeness of those manifolds and another notion of completeness specific to (G,X)-structures. In chapter 1, we also give a new proof of a theorem by Bromberg and Medina which classifies left invariant Lorentz metrics on SL(2,R) that are geodesically complete. Conjecturally, every pseudo-riemannian (G,X)-structure on a closed manifold is complete. Here we prove that it holds for certain geometries, provided that the (G,X )-structure is a priori Kleinian . This implies that, for such geometries, completeness is a closed condition. When X is a Lie group of rank 1 handled with its Killing metric, this result complements a theorem of Guéritaud–Guichard–Kassel–Wienhard, acording to which completeness is an open condition. We then turn to the study of representations of surface groups into the isometry group of a complete simply connected Riemannian manifold M of curvature less than or equal to -1. Given such a representation ρ, we prove that the set of Fuchsian representations j for which there exists a (j,ρ)-equivariant contracting map from H2 to M is a non-empty open contractible subset of the Teichmüller space (unless ρ itself is Fuchsian). This result allows us to describe the space of Lorentz metrics of constant curvature -1 on a circle bundle over a closed surface. We show that this space has finitely many connected components, classified by an invariant that we call the length of the fiber. We also prove that the total volume of those metrics only depends on the topology of the bundle and on the length of the fiber
椋野, 純一, and Junichi Mukuno. "Properly discontinuous isometric group actions on pseudo-Riemannian manifolds." Thesis, 2014. http://hdl.handle.net/2237/19977.
Full textAissiou, Tayeb. "Determinants of Pseudo-Laplacians on compact Riemannian manifolds and uniform bounds of eigenfunctions on tori." Thesis, 2013. http://spectrum.library.concordia.ca/978211/1/Aissiou_PhD_S2014.pdf.
Full textFama, Christopher J. "Non-smooth differential geometry of pseudo-Riemannian manifolds: Boundary and geodesic structure of gravitational wave space-times in mathematical relativity." Phd thesis, 1998. http://hdl.handle.net/1885/46917.
Full textMarques, André Codeço. "Rolamentos sem deslize nem torção em variedades pseudo-riemannianas." Doctoral thesis, 2015. http://hdl.handle.net/10316/26528.
Full textO objetivo fundamental desta dissertação é apresentar uma visão abrangente sobre rolamentos, sem deslize nem torção, de variedades diferenciáveis, contribuindo para aprofundar o conhecimento teórico nesta área e evidenciar potenciais aplicações. Começamos por apresentar uma definição de aplicação rolamento para o caso mais geral em que o movimento acontece dentro de espaços ambiente que são variedades pseudo-Riemannianas. Isto generaliza a definição clássica de Sharpe. A seguir, provamos algumas propriedades essenciais dos rolamentos e fazemos a ligação destes com o transporte paralelo de vetores. Dentro do contexto geral, analisamos os rolamentos das hiperquádricas de espaços pseudo-Euclidianos, com enfoque no caso dos espaços pseudo-hiperbólicos H_k^n (r). Apresentamos as equações da cinemáticas do rolamento de H_k^n (r) sobre o espaço afim associado ao espaço tangente num ponto. A obtenção de soluções explícitas destas equações é alcançada em dois casos particulares, destacando-se a situação em que o rolamento é feito ao longo de geodésicas. Rolamentos de um espaço pseudo-hiperbólico sobre outro e de pseudoesferas são igualmente tratados. Investigamos os rolamentos de grupos de Lie quadráticos sobre um espaço afim tangente. Também nestes casos se deduzem as equações da cinemática e se procuram soluções explícitas. A abordagem usada neste caso tem a preocupação de não destruir a estrutura matricial que caracteriza os elementos destes grupos matriciais. Estudamos a controlabilidade de rolamentos nos casos da hiperquádrica H_k^n (r) e dos grupos de Lie quadráticos principais, os grupos pseudo-ortogonais e os grupos simpléticos. Seguimos uma abordagem algébrica que passa por reescrever as equações da cinemática como um sistema de controlo afim a evoluir num grupo de Lie. Aplicamos os resultados obtidos anteriormente na resolução de problemas de interpolação suave em variedades e apresentamos um algoritmo interpolador. As propriedades dos rolamentos permitem transformar um problema de interpolação complicado, formulado numa variedade, num outro mais simples de resolver. São ainda fornecidos os ingredientes necessários para a implementação prática do algoritmo nos casos particulares de H_0^n (r) e H_1^n (r).
The primary goal of this dissertation is to present a comprehensive overview about rolling motions, subject to non-slip and non-twist constraints, of differentiable manifolds, contributing to deepen the theoretical knowledge in this area and to point out potential applications. We first present a definition of rolling map for the situation when the motion occurs inside an ambient space which is a pseudo-Riemannian manifold. This generalizes the classical definition of Sharpe. We then present several essential properties of rolling and make the connection between rolling motions and parallel transport of vectors. Within this general framework, we analyze the rolling of hyperquadrics embedded in pseudo-Euclidean spaces, focusing on the case of pseudo-hyperbolic spaces H_k^n (r). The kinematic equations of rolling H_k^n (r) on the affine space associated to the tangent space at a point is presented. Explicit solutions of these equations are obtained in two particular cases, with emphasis when the rolling is done along geodesics. Rolling of a pseudo-hyperbolic space on another and rolling of pseudo-spheres are equally treated. We investigate the rolling of quadratic Lie groups on an affine space tangent. We also derive the corresponding kinematic equations and look for explicit solutions. The approach used here is chosen so that the matrix structure that characterizes the elements of these matrix groups is not destroyed. We also address the controllability issue of rolling motions in the cases of hyperquadrics H_k^n (r) and of the most important quadratic Lie groups, pseudo-orthogonal groups and symplectic groups. We used an algebraic approach to controllability that requires rewriting the kinematic equations as a control system evolving on a Lie group. We apply the results previously obtained to solve problems of smooth interpolation on manifolds and present an interpolating algorithm. The properties of rolling enable to transform a complicated interpolation problem, formulated on a manifold, on another much simpler to solve. Ingredients needed to implement the algorithm are provided in the specific cases of H_0^n (r) and H_1^n (r).
Rahm, Alexander. "Characteristic classes of vector bundles with extra structure." Thesis, 2007. http://hdl.handle.net/11858/00-1735-0000-000D-F285-2.
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