Dissertations / Theses: 'Differential geometry'

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Liu, Yang, and 劉洋. "Optimization and differential geometry for geometric modeling." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2008. http://hub.hku.hk/bib/B40988077.

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Liu, Yang. "Optimization and differential geometry for geometric modeling." Click to view the E-thesis via HKUTO, 2008. http://sunzi.lib.hku.hk/hkuto/record/B40988077.

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Whiteway, L. "Topics in differential geometry." Thesis, University of Oxford, 1987. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.379896.

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Taylor, Thomas E. "Differential geometry of Minkowski spaces." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1997. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp04/mq24990.pdf.

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Lenssen, Mark. "A topic in differential geometry." Thesis, University of Oxford, 1992. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.314920.

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Guo, Guang-Yuan. "Differential geometry of holomorphic bundles." Thesis, University of Oxford, 1994. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.239283.

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Hale, Mark. "Developments in noncommutative differential geometry." Thesis, Durham University, 2002. http://etheses.dur.ac.uk/3948/.

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One of the great outstanding problems of theoretical physics is the quantisation of gravity, and an associated description of quantum spacetime. It is often argued that, at short distances, the manifold structure of spacetime breaks down and is replaced by some sort of algebraic structure. Noncommutative geometry is a possible candidate for the mathematics of this structure. However, physical theories on noncommutative spaces are still essentially classical and need to be quantised. We present a path integral formalism for quantising gravity in the form of the spectral action. Our basic principle is to sum over all Dirac operators. The approach is demonstrated on two simple finite noncommutative geometries (the two-point space and the matrix geometry M(_2)(C)) and a circle. In each case, we start with the partition function and calculate the graviton propagator and Greens functions. The expectation values of distances are also evaluated. We find on the finite noncommutative geometries, distances shrink with increasing graviton excitations, while on a circle, they grow. A comparison is made with Rovelli's canonical quantisation approach, and with his idea of spectral path integrals. We also briefly discuss the quantisation of a general Riemannian manifold. Included, is a comprehensive overview of the homological aspects of noncommutative geometry. In particular, we cover the index pairing between K-theory and K-homology, KK-theory, cyclic homology/cohomology, the Chern character and the index theorem. We also review the various field theories on noncommutative geometries.

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Bartocci, C. "Foundations of graded differential geometry." Thesis, University of Warwick, 1993. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.386972.

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Mazenc, Edward A. "Multifield inflation and differential geometry." Thesis, Massachusetts Institute of Technology, 2013. http://hdl.handle.net/1721.1/83809.

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Thesis (S.B.)--Massachusetts Institute of Technology, Dept. of Physics, 2013.
Cataloged from PDF version of thesis.
Includes bibliographical references (pages 63-67).
Cosmic inflation posits that the universe underwent a period of exponential expansion, driven by one or several quantum fields, shortly after the Big Bang. Renormalization requires the fields be non-minimally coupled to gravity. We examine such multifield models and find a rich geometric structure. After a conformal transformation of spacetime, the target field-space acquires non-trivial curvature. We explore two main consequences. First, we construct a field-space covariant framework to study quantum perturbations, extending prior work beyond the slow-roll approximation by working on the full phase space of the theory. Secondly, we show that a wide class of inflationary models can be understood as a geodesic motion on a suitably related manifold. Our geometric approach provides great insight into the (classical) field dynamics, and we have used them to compute non-gaussianities in the cosmic microwave background radiation spectrum.
by Edward A. Mazenc.
S.B.

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Zharkov, Sergei. "Conic structures in differential geometry." Thesis, Connect to e-thesis, 2000. http://theses.gla.ac.uk/1005/.

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Thesis (Ph.D.) -- University of Glasgow, 2000.
Includes bibliographical references (p.86-88). Print version also available. Mode of access : World Wide Web. System requirements : Adobe Acrobat reader required to view PDF document.

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Lu, Adonis. "Statistical Theory Through Differential Geometry." Scholarship @ Claremont, 2019. https://scholarship.claremont.edu/cmc_theses/2181.

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This thesis will take a look at the roots of modern-day information geometry and some applications into statistical modeling. In order to truly grasp this field, we will first provide a basic and relevant introduction to differential geometry. This includes the basic concepts of manifolds as well as key properties and theorems. We will then explore exponential families with applications of probability distributions. Finally, we select a few time series models and derive the underlying geometries of their manifolds.

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Nash, Oliver. "Differential geometry of monopole moduli spaces." Thesis, University of Oxford, 2006. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.437029.

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Marriott, Paul. "Applications of differential geometry to statistics." Thesis, University of Warwick, 1990. http://wrap.warwick.ac.uk/55719/.

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Chapters 1 and 2 are both surveys of the current work in applying geometry to statistics. Chapter 1 is a broad outline of all the work done so far, while Chapter 2 studies, in particular, the work of Amari and that of Lauritzen. In Chapters 3 and 4 we study some open problems which have been raised by Lauritzen's work. In particular we look in detail at some of the differential geometric theory behind Lauritzen's defmition of a Statistical manifold. The following chapters follow a different line of research. We look at a new non symmetric differential geometric structure which we call a preferred point manifold. We show how this structure encompasses the work of Amari and Lauritzen, and how it points the way to many generalizations of their results. In Chapter 5 we define this new structure, and compare it to the Statistical manifold theory. Chapter 6 develops some examples of the new geometry in a statistical context. Chapter 7 starts the development of the pure theory of these preferred point manifolds. In Chapter 8 we outline possible paths of research in which the new geometry may be applied to statistical theory. We include, in an appendix, a copy of a joint paper which looks at some direct applications of differential geometry to a statistical problem, in this case it is the problem of the behaviour of the Wald test with nonlinear restriction functions.

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West, Janet Mary. "The differential geometry of the crosscap." Thesis, University of Liverpool, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.260330.

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Davis, Declan Denis Daniel. "Affine differential geometry and singularity theory." Thesis, University of Liverpool, 2008. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.479061.

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Flari, Magdalini K. "Triple vector bundles in differential geometry." Thesis, University of Sheffield, 2018. http://etheses.whiterose.ac.uk/21385/.

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The triple tangent bundle T3M of a manifold M is a prime example of a triple vector bundle. The definition of a general triple vector bundle is a cube of vector bundles that commute in the strict categorical sense. We investigate the intrinsic features of such cubical structures, introducing systematic notation, and further studying linear double sections; a generalization of sections of vector bundles. A set of three linear double sections on a triple vector bundle E yields a total of six different routes from the base manifold M of E to the total space E. The underlying commutativity of the vector bundle structures of E leads to the concepts of warp and ultrawarp, concepts that measure the noncommutativity of the six routes. The main theorem shows that despite this noncommutativity, there is a strong relation between the ultrawarps. The methods developed to prove the theorem rely heavily on the analysis of the core double vector bundles and of the ultracore vector bundle of E. This theorem provides a conceptual proof of the Jacobi identity, and a new interpretation of the curvature of a connection on a vector bundle A.

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Hadnot, Jason. "Differential geometry of Fermat quartic surface." Thesis, Boston University, 2013. https://hdl.handle.net/2144/12773.

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Thesis (Ph.D.)--Boston University PLEASE NOTE: Boston University Libraries did not receive an Authorization To Manage form for this thesis or dissertation. It is therefore not openly accessible, though it may be available by request. If you are the author or principal advisor of this work and would like to request open access for it, please contact us at open-help@bu.edu. Thank you.
We examine the differential geometry of the Fermat Quartic surface X4/0+X4/3-X4/1-X4/2 = 0 in CP^3 with induced Fubini-Study metric. We show that the differential equations of geodesics, when restricted to the real Fermat quartic surface inside the full complex quartic, can be reduced to two non-linear differential equations with rational coefficients along especially chosen geodesics. This simplification opens up the possibility of parametrizing these geodesics in terms of genus three Abelian integrals and their inversions. Furthermore the identity component of the differential Galois group of normal variational equation, derived from the geodesic equation along one of these selected curves, is SL(2,C). By Morales-Ramis theory the Hamiltonian system defining the geodesic equations is not integrable in a neighborhood of this solution by meromorphic integrals.

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Narayanan, Vivek. "Some aspects of the geometry of Poisson dynamical systems." Access restricted to users with UT Austin EID Full text (PDF) from UMI/Dissertation Abstracts International, 2001. http://wwwlib.umi.com/cr/utexas/fullcit?p3038192.

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Milhorat, Jean-Louis. "Sur les connexions conformes." Grenoble 2 : ANRT, 1986. http://catalogue.bnf.fr/ark:/12148/cb375996942.

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Ronchi, Elena. "The notion of curvature in differential geometry." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2021.

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In questo lavoro ci occupiamo di studiare la geometria differenziale delle superfici con un'attenzione particolare al concetto di curvatura. Nel primo capitolo studieremo le superfici, in particolare, immerse in spazi Euclidei utilizzando un approccio più semplice e concreto. Nel secondo capitolo introdurremo la nozione di forma differenziale e la applicheremo nello studio delle superfici all'interno degli spazi Euclidei attraverso il metodo dei moving frames. Presenteremo anche una generalizzazione del concetto di superficie, vale a dire ciò che chiameremo varietà differenziabile. Infine nel terzo capitolo introdurremo un terzo approccio più astratto, quello della geometria riemanniana, focalizzandoci in particolare sulla nozione di curvatura.

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Duran, James Joseph. "Differential geometry of surfaces and minimal surfaces." CSUSB ScholarWorks, 1997. https://scholarworks.lib.csusb.edu/etd-project/1542.

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Bousfield, R. A. "Applications of differential geometry to structural mechanics." Thesis, University of Hertfordshire, 1986. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.372544.

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Holanda, Felipe D'Angelo. "Introduction to differential geometry of plane curves." Universidade Federal do CearÃ, 2015. http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=15052.

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CoordenaÃÃo de AperfeÃoamento de Pessoal de NÃvel Superior
A intenÃÃo desse trabalho serÃ de abordar de forma bÃsica e introdutÃria o estudo da Geometria Diferencial, que por sua vez tem seus estudos iniciados com as Curvas Planas. SerÃ necessÃrio um conhecimento de CÃlculo Diferencial, Integral e Geometria AnalÃtica para melhor compreensÃo desse trabalho, pois como seu prÃprio nome nos transparece Geometria Diferencial vem de uma junÃÃo do estudo da Geometria envolvendo CÃlculo. Assim abordaremos subtemas como curvas suaves, vetor tangente, comprimento de arco passando por fÃrmulas de Frenet, curvas evolutas e involutas e finalizaremos com alguns teoremas importantes, como o teorema fundamental das curvas planas, teorema de Jordan e o teorema dos quatro vÃrtices. O que, basicamente representa, o capÃtulo 1, 4 e 6 do livro IntroduÃÃo Ãs Curvas Planas de HilÃrio Alencar e Walcy Santos.
The intention of this work is to address in basic form and introductory study of Differential Geometry, which in turn has started his studies with Planas curves. It will require a knowledge of Differential Calculus, Integral and Analytic Geometry for better understanding of this work, because as its name says in Differential Geometry comes from the joint study of geometry involving Calculation. So we discuss sub-themes as smooth curves, tangent vector, arc length through formulas of Frenet, evolutas curves and involute and conclude with some important theorems, as the fundamental theorem of plane curves, Jordan 's theorem and the theorem of four vertices. What basically is, Chapter 1, 4 and 6 of the book Introduction to Plane Curves HilÃrio Alencar and Walcy Santos.

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Dangskul, Supreedee. "Construction of Seifert surfaces by differential geometry." Thesis, University of Edinburgh, 2016. http://hdl.handle.net/1842/20382.

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A Seifert surface for a knot in ℝ³ is a compact orientable surface whose boundary is the knot. Seifert surfaces are not unique. In 1934 Herbert Seifert provided a construction of such a surface known as the Seifert Algorithm, using the combinatorics of a projection of the knot onto a plane. This thesis presents another construction of a Seifert surface, using differential geometry and a projection of the knot onto a sphere. Given a knot K : S¹⊂ R³, we construct canonical maps F : ΛdiffS² → ℝ=4πZ and G : ℝ³ - K(S¹) → ΛdiffS² where ΛdiffS² is the space of smooth loops in S². The composite FG : ℝ³ - K(S¹) → ℝ=4πZ is a smooth map defined for each u∈2 ℝ³ - K(S¹) by integration of a 2- form over an extension D² → S² of G(u) : S1 → S². The composite FG is a surjection which is a canonical representative of the generator 1∈H¹(ℝ³- K(S¹)) = Z. FG can be defined geometrically using the solid angle. Given u ∈ ℝ³ - K(S¹), choose a Seifert surface Σu for K with u ∉ Σu. It is shown that FG(u) is equal to the signed area of the shadow of Σu on the unit sphere centred at u. With this, FG(u) can be written as a line integral over the knot. By Sard's Theorem, FG has a regular value t ∈ ℝ=4πZ. The behaviour of FG near the knot is investigated in order to show that FG is a locally trivial fibration near the knot, using detailed differential analysis. Our main result is that (FG)-¹(t)⊂ ℝ³ can be closed to a Seifert surface by adding the knot.

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Clarke, Daniel. "Integrability in submanifold geometry." Thesis, University of Bath, 2012. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.558890.

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This thesis concerns the relationship of submanifold geometry, in both the smooth and discrete sense, to representation theory and the theory of integrable systems. We obtain Lie theoretic generalisations of the transformation theory of projectively and Lie applicable surfaces, and M�obius-flat submanifolds of the conformal n-sphere. In the former case, we propose a discretisation. We develop a projective approach to centro-ane hypersurfaces, analogous to the conformal approach to submanifolds in spaceforms. This yields a characterisation of centro-ane hypersurfaces amongst M�obius-flat projective hypersurfaces using polynomial conserved quantities. We also propose a discretisation of curved flats in symmetric spaces. After developing the transformation theory for this, we see how Darboux pairs of discrete isothermicnets arise as discrete curved flats in the symmetric space of opposite point pairs. We show how discrete curves in the 2-sphere fit into this framework.

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Pinsky, Nathan. "Mathematical Knowledge for Teaching and Visualizing Differential Geometry." Scholarship @ Claremont, 2013. http://scholarship.claremont.edu/hmc_theses/49.

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In recent decades, education researchers have recognized the need for teachers to have a nuanced content knowledge in addition to pedagogical knowledge, but very little research was conducted into what this knowledge would entail. Beginning in 2008, math education researchers began to develop a theoretical framework for the mathematical knowledge needed for teaching, but their work focused primarily on elementary schools. I will present an analysis of the mathematical knowledge needed for teaching about the regular curves and surfaces, two important concepts in differential geometry which generalize to the advanced notion of a manifold, both in a college classroom and in an on-line format. I will also comment on the philosophical and political questions that arise in this analysis.

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McCormick, Andrew Grady. "Discrete Differential Geometry and Physics of Elastic Curves." Thesis, Harvard University, 2013. http://dissertations.umi.com/gsas.harvard:11121.

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Bakker, Craig Kent Reddick. "A differential geometry framework for multidisciplinary design optimization." Thesis, University of Cambridge, 2015. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.708688.

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Pitucco, Anthony Peter. "Differential-geometric aspects of adapted contact structures." Diss., The University of Arizona, 1991. http://hdl.handle.net/10150/185532.

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Let M denote a 2n-dimensional globally defined orientable manifold from which is constructed the product space N = M x R. It is assumed that N is endowed with a set of 2n independent smooth 1-forms {π(h),πʰ:h = 1,..,n}. Certain conditions are imposed on {π(h),πʰ} which imply the existence of local coordinates {qʰ,p(h)} on M and a function H(qʰ,p(h),t) on N, where t is the single coordinate on R, such that dπ = π(h) ∧ πʰ, where π has the structure of a Cartan form on N. The assumption that the function h = p(h)∂H/∂p(h)-H is non-zero on a region D ⊂ N, implies that π has maximal class on D. This construction gives rise to a local adapted contact structure on N and a local symplectic structure on M. A vector field X on N is said to be a contact field if there exists a smooth function σ : N → R such that ₤ₓπ = σπ. A vector field Z on N is called a canonical vector field if it admits the representation Z = ∂/∂t + (H, ) where (,) denotes the Poisson bracket on M. For a given function σ, a prescription is given for the construction of the space c(σ)(N) of contact fields in terms of solutions F of the p.d.e. Z = σh. The vector space (UNFORMATTED EQUATION FOLLOWS) c(N) = ∪ (σ∊C)(∞)c(σ)(N) (END UNFORMATTED EQUATION) is shown to have the structure of a Lie sub-algebra of the Lie algebra of vector fields on N. It is shown that the associated subspace A(π) = {X:X˩π = 0} is such that c(σ)(N) ∩ A(π) = {0}. This implies that there is an X in c(σ)(N) such that X˩π ≠ 0. Thus, if the function H that appears in the Cartan form π is such that H = X˩π for any X ∊ c(σ)(N) it is possible to deduce that ∂H/∂t ≠ 0, which shows that such vector fields may be of relevance to the theory of non-conservative systems. A different set of 2n 1-forms {π(h),πʰ} is introduced on N that are subject to analogous conditions which ensure the existence of local coordinates (qʰ,p(h)) on M and a function K(qʰ,p(h),t) that gives rise to a new Cartan form π on N such that dπ= π(h) ∧ πʰ. By definition, the fundamental invariant of a parameter-dependent canonical transformation on N is dπ = dπ. In this new setting a contact field X satisfies the ₤ₓπ = σπ for some function σ: N to R. The relationship between the contact vector fields X and X is investigated in depth.

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Swann, Andrew F. "Hyperkähler and quaternionic Kähler geometry." Thesis, University of Oxford, 1990. http://ora.ox.ac.uk/objects/uuid:bb301f35-25e0-445d-8045-65e402908b85.

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A quaternion-Hermitian manifold, of dimension at least 12, with closed fundamental 4-form is shown to be quaternionic Kähler. A similar result is proved for 8-manifolds. HyperKähler metrics are constructed on the fundamental quaternionic line bundle (with the zero-section removed) of a quaternionic Kähler manifold (indefinite if the scalar curvature is negative). This construction is compatible with the quaternionic Kähler and hyperKähier quotient constructions and allows quaternionic Kähler geometry to be subsumed into the theory of hyperKähler manifolds. It is shown that the hyperKähler metrics that arise admit a certain type of SU(2)- action, possess functions which are Kähler potentials for each of the complex structures simultaneously and determine quaternionic Kähler structures via a variant of the moment map construction. Quaternionic Kähler metrics are also constructed on the fundamental quaternionic line bundle and a twistor space analogy leads to a construction of hyperKähler metrics with circle actions on complex line bundles over Kähler-Einstein (complex) contact manifolds. Nilpotent orbits in a complex semi-simple Lie algebra, with the hyperKähler metrics defined by Kronheimer, are shown to give rise to quaternionic Kähler metrics and various examples of these metrics are identified. It is shown that any quaternionic Kähler manifold with positive scalar curvature and sufficiently large isometry group may be embedded in one of these manifolds. The twistor space structure of the projectivised nilpotent orbits is studied.

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Akıncı, Figen Pashaev Oktay K. "Geometry of moving curves and soliton equations/." [s.l.]: [s.n.], 2004. http://library.iyte.edu.tr/tezler/master/matematik/T000454.pdf.

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Lord, Steven. "Riemannian non-commutative geometry /." Title page, abstract and table of contents only, 2002. http://web4.library.adelaide.edu.au/theses/09PH/09phl8661.pdf.

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White, Edward C. Jr. "Polar - legendre duality in convex geometry and geometric flows." Thesis, Atlanta, Ga. : Georgia Institute of Technology, 2008. http://hdl.handle.net/1853/24689.

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Calin, Ovidiu. "The missing direction and differential geometry on Heisenberg manifolds." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2000. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp02/NQ53779.pdf.

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Nystrom, Michel. "The Ambrose-Palais-Singer theorem in synthetic differential geometry /." Thesis, McGill University, 1987. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=66260.

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Eastlick, Mark Thomas. "Discrete differential geometry and an application in multiresolution analysis." Thesis, University of Sheffield, 2006. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.434535.

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Brzezinski, Tomasz. "Differential geometry of quantum groups and quantum fibre bundles." Thesis, University of Cambridge, 1994. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.321113.

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Jacobs, Andrew D. "Nonstandard quantum groups : twisting constructions and noncommutative differential geometry." Thesis, University of St Andrews, 1998. http://hdl.handle.net/10023/13693.

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The general subject of this thesis is quantum groups. The major original results are obtained in the particular areas of twisting constructions and noncommutative differential geometry. Chapters 1 and 2 are intended to explain to the reader what are quantum groups. They are written in the form of a series of linked results and definitions. Chapter 1 reviews the theory of Lie algebras and Lie groups, focusing attention in particular on the classical Lie algebras and groups. Though none of the quoted results are due to the author, such a review, aimed specifically at setting up the paradigm which provides essential guidance in the theory of quantum groups, does not seem to have appeared already. In Chapter 2 the elements of the quantum group theory are recalled. Once again, almost none of the results are due to the author, though in Section 2.10, some results concerning the nonstandard Jordanian group are presented, by way of a worked example, which have not been published. Chapter 3 concerns twisting constructions. We introduce a new class of 2-cocycles defined explicitly on the generators of certain multiparameter standard quantum groups. These allow us, through the process of twisting the familiar standard quantum groups, to generate new as well as previously known examples of non-standard quantum groups. In particular we are able to construct generalisations of both the Cremmer-Gervais deformation of SL(3) and the so called esoteric quantum groups of Fronsdal and Galindo in an explicit and straightforward manner. In Chapter 4 we consider the differential calculus on Hopf algebras as introduced by Woronowicz. We classify all 4-dimensional first order bicovariant calculi on the Jordanian quantum group GL[sub]h,[sub]g(2) and all 3-dimensional first order bicovariant calculi on the Jordanian quantum group SL[sub]h(2). In both cases we assume that the bicovariant bimodules are generated as left modules by the differentials of the quantum group generators. It is found that there are 3 1-parameter families of 4-dimensional bicovariant first order calculi on GL[sub]h,[sub]g(2) and that there is a single, unique, 3-dimensional bicovariant calculus on SL[sub]h(2). This 3-dimensional calculus may be obtained through a classical-like reduction from any one of the three families of 4-dimensional calculi on GL[sub]h,[sub]g(2). Details of the higher order calculi and also the quantum Lie algebras are presented for all calculi. The quantum Lie algebra obtained from the bicovariant calculus on SL[sub]h(2) is shown to be isomorphic to the quantum Lie algebra we obtain as an ad-submodule within the Jordanian universal enveloping algebra U[sub]h(sl[sub]2(C)) and also through a consideration of the decomposition of the tensor product of two copies of the deformed adjoint module. We also obtain the quantum Killing form for this quantum Lie algebra.

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Legostova, Ye. "On subharmonic functions and differential geometry in the large." Thesis, Сумський державний університет, 2014. http://essuir.sumdu.edu.ua/handle/123456789/35035.

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This issue is proffesor H. Hopf. He drew our attention to the connection between differential geometry and potential theory which is revealed by relations (1.3) and (1.4). For example, the function u(x,y) is subharmonic in a certain (x,у)-parameter region if and only if in the corresponding domain on M. This fact had already been used by E. F. Beckenbach and T. Rado in their proof of the isoperimetric inequality on surfaces of negative curvature. Analogously, и is super-harmonic if and only if . Furthermore, (1.4) discloses an even deeper connection: The surface integral of К, considered as a set function, is essentially the measure associated with и. Consequently, results of differential geometry in the large involving the curvatura integra, such as those due to S. Cohn- Vossen, F. Fiala, Ch. Blanc and F. Fiala, have a potentialtheoretical meaning. It is therefore natural to apply functiontheoretical methods to this field in the hope that not only other (and eventually simpler) proofs of known results will be found, but also theorems which are new in both their differential geometrical and potential-theoretical aspects. When you are citing the document, use the following link http://essuir.sumdu.edu.ua/handle/123456789/35035

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Baker, Andrew. "Applications of differential geometry to high spin field theories." Thesis, Aston University, 1990. http://publications.aston.ac.uk/10645/.

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The main aim of this thesis is to investigate the application of methods of differential geometry to the constraint analysis of relativistic high spin field theories. As a starting point the coordinate dependent descriptions of the Lagrangian and Dirac-Bergmann constraint algorithms are reviewed for general second order systems. These two algorithms are then respectively employed to analyse the constraint structure of the massive spin-1 Proca field from the Lagrangian and Hamiltonian viewpoints. As an example of a coupled field theoretic system the constraint analysis of the massive Rarita-Schwinger spin-3/2 field coupled to an external electromagnetic field is then reviewed in terms of the coordinate dependent Dirac-Bergmann algorithm for first order systems. The standard Velo-Zwanziger and Johnson-Sudarshan inconsistencies that this coupled system seemingly suffers from are then discussed in light of this full constraint analysis and it is found that both these pathologies degenerate to a field-induced loss of degrees of freedom. A description of the geometrical version of the Dirac-Bergmann algorithm developed by Gotay, Nester and Hinds begins the geometrical examination of high spin field theories. This geometric constraint algorithm is then applied to the free Proca field and to two Proca field couplings; the first of which is the minimal coupling to an external electromagnetic field whilst the second is the coupling to an external symmetric tensor field. The onset of acausality in this latter coupled case is then considered in relation to the geometric constraint algorithm.

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Athanasopoulos, Michael, Hassan Ugail, and Castro Gabriela Gonzalez. "Parametric design of aircraft geometry using partial differential equations." Elsevier, 2009. http://hdl.handle.net/10454/2725.

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42

Strawn, Nathaniel Kirk. "Geometry and constructions of finite frames." [College Station, Tex. : Texas A&M University, 2007. http://hdl.handle.net/1969.1/ETD-TAMU-1335.

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43

Schelp, Richard Charles. "The standard model and beyond in noncommutative geometry /." Digital version accessible at:, 2000. http://wwwlib.umi.com/cr/utexas/main.

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44

Masmali, Ibtisam Ali. "Hopf algebra and noncommutative differential structures." Thesis, Swansea University, 2010. https://cronfa.swan.ac.uk/Record/cronfa42676.

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In this thesis I will study noncommutative differential geometry, after the style of Connes and Woronowicz. In particular two examples of differential calculi on Hopf algebras are considered, and their associated covariant derivatives and Riemannian geometry. These are on the Heisenberg group, and on the finite group A4. I consider bimodule connections after the work of Madore. In the last chapter noncommutative fibrations are considerd, with an application to the Leray spectral sequence. NOTATION. In this thesis equations are numbered as round brackets (), where (a.b) denotes equation b in chapter a, and references are indicated by square brackets []. This thesis has been typeset using Latex, and some figures using the Visio program.

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Moreira, Ana Claudia da Silva. "O metodo do referencial movel via exemplos." [s.n.], 2009. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306816.

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Orientador: Carlos Eduardo Duran Fernandez
Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica
Made available in DSpace on 2018-08-13T06:35:44Z (GMT). No. of bitstreams: 1 Moreira_AnaClaudiadaSilva_M.pdf: 1048893 bytes, checksum: 74079b9ae1dc0f7d9eee36e181cf4377 (MD5) Previous issue date: 2009
Resumo: O presente trabalho tem por objetivo estudar o Método do Referencial Móvel de Cartan aplicado a curvas, através de diversos exemplos, desde problemas simples, passando por publicações dos anos 60 e 70 até artigos recentes. Embora existam teorias gerais para encontrar referenciais de Cartan, optamos por estudar uma forma um pouco mais "artesanal" de construção dos referenciais móveis; a ênfase está na absorção das variadas técnicas e intuições que se adaptam a cada geometria
Abstract: The aim of this work is to present the Cartan's Moving Frame Method applied to curves, through several examples, starting with simple problems, going through publications of the 60's, 70's, and up to recent results. Although there are general theories for finding Cartan's moving frames, we chose to study a slightly more "handcraft" way of building the required moving frame; the emphasis being on the absorption of the different techniques and intuitive understanding adapted to each geometry
Mestrado
Mestre em Matemática

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46

Botnan, Magnus Bakke. "Three Approaches in Computational Geometry and Topology : Persistent Homology, Discrete Differential Geometry and Discrete Morse Theory." Thesis, Norges teknisk-naturvitenskapelige universitet, Institutt for matematiske fag, 2011. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-14201.

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We study persistent homology, methods in discrete differential geometry and discrete Morse theory. Persistent homology is applied to computational biology and range image analysis. Theory from differential geometry is used to define curvature estimates of triangulated hypersurfaces. In particular, a well-known method for triangulated surfacesis generalised to hypersurfaces of any dimension. The thesis concludesby discussing a discrete analogue of Morse theory.

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Kirchhoff-Lukat, Charlotte Sophie. "Aspects of generalized geometry : branes with boundary, blow-ups, brackets and bundles." Thesis, University of Cambridge, 2018. https://www.repository.cam.ac.uk/handle/1810/283007.

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This thesis explores aspects of generalized geometry, a geometric framework introduced by Hitchin and Gualtieri in the early 2000s. In the first part, we introduce a new class of submanifolds in stable generalized complex manifolds, so-called Lagrangian branes with boundary. We establish a correspondence between stable generalized complex geometry and log symplectic geometry, which allows us to prove results on local neighbourhoods and small deformations of this new type of submanifold. We further investigate Lefschetz thimbles in stable generalized complex Lefschetz fibrations and show that Lagrangian branes with boundary arise in this context. Stable generalized complex geometry provides the simplest examples of generalized complex manifolds which are neither complex nor symplectic, but it is sufficiently similar to symplectic geometry for a multitude of symplectic results to generalize. Our results on Lefschetz thimbles in stable generalized complex geometry indicate that Lagrangian branes with boundary are part of a potential generalisation of the Wrapped Fukaya category to stable generalized complex manifolds. The work presented in this thesis should be seen as a first step towards the extension of Floer theory techniques to stable generalized complex geometry, which we hope to develop in future work. The second part of this thesis studies Dorfman brackets, a generalisation of the Courant- Dorfman bracket, within the framework of double vector bundles. We prove that every Dorfman bracket can be viewed as a restriction of the Courant-Dorfman bracket on the standard VB-Courant algebroid, which is in this sense universal. Dorfman brackets have previously not been considered in this context, but the results presented here are reminiscent of similar results on Lie and Dull algebroids: All three structures seem to fit into a more general duality between subspaces of sections of the standard VB-Courant algebroid and brackets on vector bundles of the form T M ⊕ E ∗ , E → M a vector bundle. We establish a correspondence between certain properties of the brackets on one, and the subspaces on the other side.

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Kemp, M. C. "Geometric Seifert 4-manifolds with aspherical bases." University of Sydney. Mathematics, 2005. http://hdl.handle.net/2123/702.

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Seifert fibred 3-manifolds were originally defined and classified by Seifert. Scott gives a survey of results connected with these classical Seifert spaces, in particular he shows they correspond to 3-manifolds having one of six of the eight 3-dimensional geometries (in the sense of Thurston). Essentially, a classical Seifert manifold is a S1-bundle over a 2-orbifold. More generally, a Seifert manifold is the total space of a bundle over a 2-orbifold with flat fibres. It is natural to ask if these generalised Seifert manifolds describe geometries of higher dimension. Ue has considered the geometries of orientable Seifert 4-manifolds (which have general fibre a torus). He proves that (with a finite number of exceptions orientable manifolds of eight of the 4-dimensional geometries are Seifert fibred. However, Seifert manifolds with a hyperbolic base are not necessarily geometric. In this paper, we seek to extend Ue's work to the non-orientable case. Firstly, we will show that Seifert spaces over an aspherical base are determined (up to fibre preserving homeomorphism) by their fundamental group sequence. Furthermore when the base is hyperbolic, a Seifert space is determined (up to fibre preserving homeomorphism) by its fundamental group. This generalises the work of Zieschang, who assumed the base has no reflector curves, the fibre was a torus and that a monodromy of a loop surrounding a cone point is trivial. Then we restrict to the 4 dimensional case and find necessary and sufficient conditions for Seifert 4 manifolds over hyperbolic or Euclidean orbifolds to be geometric in the sense of Thurston. Ue proved that orientable Seifert 4-manifolds with hyperbolic base are geometric if and only if the monodromies are periodic, and we will prove that we can drop the orientable condition. Ue also proved that orientable Seifert 4-manifolds with a Euclidean base are always geometric, and we will again show the orientable assumption is unnecessary.

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Adiprasito, Karim Alexander [Verfasser]. "Methods from Differential Geometry in Polytope Theory / Karim Alexander Adiprasito." Berlin : Freie Universität Berlin, 2013. http://d-nb.info/103640661X/34.

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Lee, Chih-kuo. "Robust evaluation of differential geometry properties using interval arithmetic techniques." Thesis, Massachusetts Institute of Technology, 2005. http://hdl.handle.net/1721.1/33565.

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Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Ocean Engineering, 2005.
Includes bibliographical references (p. 79-82).
This thesis presents a robust method for evaluating differential geometry properties of sculptured surfaces by using a validated ordinary differential equation (ODE) system solver based on interval arithmetic. Iso-contouring of curvature of a Bezier surface patch. computation of curvature lines of a Bezier surface patch and computation of geodesics of a Bezier surface patch are computed by the Validated Numerical Ordinary Differential Equations (VNODE) solver which employs rounded interval arithmetic methods. Then. the results generated from the VNODE program are compared with the results from Praxiteles code which uses non-validated ODE solvers operating in double precision floating point arithmetic for the solution of the same problems. From the results of these experiments, we find that the VNODE program performs these computations reliably, but at increased computational cost.
by Chih-kuo Lee.
S.M.

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Dissertations / Theses on the topic 'Differential geometry'

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