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Dissertations / Theses on the topic 'Tangent bundles'

Author: Grafiati

Published: 4 June 2021

Last updated: 31 July 2024

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1

Tureli, Sina. "Integrability of Continuous Tangent Sub-bundles." Doctoral thesis, SISSA, 2015. http://hdl.handle.net/20.500.11767/4876.

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In this thesis, the main aim is to study the integrability properties of continuous tangent sub-bundles, especially those that arise in the study of dynamical systems. After the introduction and examples part we start by studying integrability of such sub-bundles under different regularity and dynamical assumptions. Then we formulate a continuous version of the classical Frobenius theorem and state some applications to such bundles, to ODE and PDE. Finally we close of by stating some ongoing work related to interactions between integrability, sub-Riemannian geometry and contact geometry.

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2

Hindeleh, Firas. "Tangent and cotangent bundles automorphism groups and representations of Lie groups /." See Full Text at OhioLINK ETD Center (Requires Adobe Acrobat Reader for viewing), 2006. http://www.ohiolink.edu/etd/view.cgi?acc_num=toledo1153933389.

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Thesis (Ph.D.)--University of Toledo, 2006.
Typescript. "A dissertation [submitted] as partial fulfillment of the requirements of the Doctor of Philosophy degree in Mathematics." Bibliography: leaves 79-82.

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3

Hindeleh, Firas Y. "Tangent and Cotangent Bundles, Automorphism Groups and Representations of Lie Groups." University of Toledo / OhioLINK, 2006. http://rave.ohiolink.edu/etdc/view?acc_num=toledo1153933389.

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4

Wang, Hongyuan. "On a class of algebraic surfaces with numerically effective cotangent bundles." Columbus, Ohio : Ohio State University, 2006. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1154450131.

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5

Pavolaitė, Miglė. "Simetrinės trečiosios eilės liestinės sluoksniuotės." Master's thesis, Lithuanian Academic Libraries Network (LABT), 2010. http://vddb.laba.lt/obj/LT-eLABa-0001:E.02~2010~D_20100709_091446-82031.

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Darbe nagrinėjamos simetrinės trečiosios eilės liestinės sluoksniuotės, kurios apibrėžiamos kaip 3 - džetų aibės. Surasta simetrinės erdvės izotropijų grupė, o taip pat jos izomorfijų grupė. Gautos izomorfijų grupės struktūrinės lygtys, surasti erdvės Maurerio – Kartano lygčių analogai, įrodytos formulės, išreiškiančios indukuotosios afiniosios sieties kreivumo tenzorių komponentes izomorfijų grupės struktūrinėmis konstantomis. Taip pat gauta visa eilė tapatybių, siejančių kreivumo objektus ir izomorfijų grupės struktūrines konstantas (apibendrintos Ričio ir Bianchi tapatybės).
The paper examined the symmetric third order tangent bundle, defined as 3- jet space. Found symmetric space isotropy group, as well as its isomorphy group. The resulting structural equation of isomorphy group, find this area Maurer - Cartan analogues of equations, an established formula, expressing inducted affines connection component of curvature tensors of the isomorphy group structural constants. Also received identities connecting the curvature objects structural constants of isomorphy group (generalized in Riči and Bianchi identity).

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6

Mickutė, Laura. "Apie trečios eilės liestinių sluoksniuočių geometriją." Master's thesis, Lithuanian Academic Libraries Network (LABT), 2005. http://vddb.library.lt/obj/LT-eLABa-0001:E.02~2005~D_20050623_101559-72938.

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In this work is analysed the tangent bundle geometry order 3. Those bundles are defined like 3 - jet space. Co - ordinates transformation formulas of those bundles are received, how the object of linear connection inducted affine connections is demonstrated. In this work the theorem how the object of linear connection of tangent bundle inducted linear connection of tangent bundle order 3 is proved.

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7

Silva, Rafael Barbosa da. "Existência de conexões versus módulos projetivos." Universidade Federal da Paraíba, 2013. http://tede.biblioteca.ufpb.br:8080/handle/tede/7424.

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Made available in DSpace on 2015-05-15T11:46:16Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 578974 bytes, checksum: e512f47deae8cd03667ae8e7c2143b34 (MD5) Previous issue date: 2013-05-03
Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES
The notions of connection and covariant derivative has its origin in the field of Riemannian geometry , where there is no distinction between them. In fact, in this study we found that these notions are equivalent if we consider modules over K-algebras of finite type. We also show that the existence of connections implies the existence of covariant derivative. The main goal of this study is to determine which modules admit connections. We easily verified that the projective modules admit connections. In fact, they form an affine space. But we also display a module that is not projective and has connection. Later, inspired by Swan's theorem, we explore in a straightforward way modules formed by sections of the tangent bundle of some surfaces in 3-dimensional real space. Finally, we study the notion of connection introduced by Alain Connes in modules over K-algebras not necessarily commutative. And we find in that context that the modules that have connection are exactly the projectives modules.
As noções de conexão e derivada covariante tem sua origem na área de geometria riemanniana, onde não existe distinção entre elas. De fato, nós verificamos neste trabalho, que estas noções são equivalentes se considerarmos módulos sobre K-álgebras comutativas de tipo finito. Também mostramos que a existência de conexões implica na existência de derivada covariante. O objetivo central deste trabalho é determinar que módulos admitem conexão. Verificamos facilmente que os módulos projetivos admitem conexões. De fato, elas formam um espaço afim. Mas também exibimos um módulo não projetivo que possui conexão. Posteriormente, inspirados pelo teorema de Swan, exploramos de maneira direta os módulos formados pelas seções do fibrado tangente de algumas superfícies no espaço 3- dimensional real. Por fim, estudamos a noção de conexão introduzida por Alain Connes em módulos sobre K-álgebras não necessariamente comutativas. E verificamos nesse contexto que os módulo que admitem conexão são exatamente os módulos projetivos.

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8

Kravčenkaitė, Deimantė. "Euklido erdvės liečiamojo pluošto hiperpaviršių struktūra ir geometrinė prasmė." Master's thesis, Lithuanian Academic Libraries Network (LABT), 2012. http://vddb.laba.lt/obj/LT-eLABa-0001:E.02~2012~D_20120702_110845-55808.

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Šis darbas pratęsia 2010 m. autorės atlikto bakalauro darbo „Elipsinio tipo B-erdvių beveik kontaktiniai metriniai hiperpaviršiai“ tyrinėjimus, apibendrina šio darbo rezultatus kitų tipų ir rūšių -struktūroms ir pritaiko juos liečiamųjų sluoksniuočių paviršių teorijoje.
In the work, the generalized (φ, ξ, η, g)-structures in normalized hypersurfaces M2n-1 T(En) are found and its properties are investigated. Geometric meaning in basis En of some interesting hypersurfaces (hypersphere, hyperplane, hypercone,…) is explained.

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9

Simsir, Muazzez Fatma. "Conformal Vector Fields With Respect To The Sasaki Metric Tensor Field." Phd thesis, METU, 2005. http://etd.lib.metu.edu.tr/upload/12605857/index.pdf.

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On the tangent bundle of a Riemannian manifold the most natural choice of metric tensor field is the Sasaki metric. This immediately brings up the question of infinitesimal symmetries associated with the inherent geometry of the tangent bundle arising from the Sasaki metric. The elucidation of the form and the classification of the Killing vector fields have already been effected by the Japanese school of Riemannian geometry in the sixties. In this thesis we shall take up the conformal vector fields of the Sasaki metric with the help of relatively advanced techniques.

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10

Bauer, David. "Towards Discretization by Piecewise Pseudoholomorphic Curves." Doctoral thesis, Universitätsbibliothek Leipzig, 2014. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-132065.

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This thesis comprises the study of two moduli spaces of piecewise J-holomorphic curves. The main scheme is to consider a subdivision of the 2-sphere into a collection of small domains and to study collections of J-holomorphic maps into a symplectic manifold. These maps are coupled by Lagrangian boundary conditions. The work can be seen as finding a 2-dimensional analogue of the finite-dimensional path space approximation by piecewise geodesics on a Riemannian manifold (Q,g). For a nice class of target manifolds we consider tangent bundles of Riemannian manifolds and symplectizations of unit tangent bundles. Via polarization they provide a rich set of Lagrangians which can be used to define appropriate boundary value problems for the J-holomorphic pieces. The work focuses on existence theory as a pre-stage to global questions such as combinatorial refinement and the quality of the approximation. The first moduli space of lifted type is defined on a triangulation of the 2-sphere and consists of disks in the tangent bundle whose boundary projects onto geodesic triangles. The second moduli space of punctured type is defined on a circle packing domain and consists of boundary punctured disks in the symplectization of the unit tangent bundle. Their boundary components map into single fibers and at punctures the disks converge to geodesics. The coupling boundary conditions are chosen such that the piecewise problem always is Fredholm of index zero and both moduli spaces only depend on discrete data. For both spaces existence results are established for the J-holomorphic pieces which hold true on a small scale. Each proof employs a version of the implicit function theorem in a different setting. Here the argument for the moduli space of punctured type is more subtle. It rests on a connection to tropical geometry discovered by T. Ekholm for 1-jet spaces. The boundary punctured disks are constructed in the vicinity of explicit Morse flow trees which correspond to the limiting objects under degeneration of the boundary condition.

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11

Jelena, Stojanov. "Anisotropic frameworks for dynamical systems and image processing." Phd thesis, Univerzitet u Novom Sadu, Prirodno-matematički fakultet u Novom Sadu, 2015. https://www.cris.uns.ac.rs/record.jsf?recordId=93698&source=NDLTD&language=en.

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The research topic of this PhD thesis is a comparative analysis of classical specic geometric frameworks and of their anisotropic extensions; the construction of three different types of Finsler frameworks, which are suitable for the analysis of the cancer cells population dynamical system; the development of the anisotropic Beltrami framework theory with the derivation of the evolution ow equations corresponding to different classes of anisotropic metrics, and tentative applications in image processing.
Predmet istraživanja doktorske disertacije je uporedna analiza klasičnih i specifičnih geometrijskih radnih okruženja i njihovih anizotropnih proširenja; konstrukcija tri Finslerova radna okruženja različitog tipa koja su pogodna za analizu dinamičkog sistema populacije kanceroznih ćelija; razvoj teorije anizotropnog Beltramijevog radnog okruženja i formiranje jednačina evolutivnog toka za različite klase anizotropnih metrika, kao i mogućnost primene dobijenih teorijskih rezultata u digitalnoj obradi slika.

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12

Prasannakumar, K. N. "The theory of curvatures, tangent bundles and normal bundles in M H D." Thesis, 1986. http://hdl.handle.net/2009/2669.

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13

Toko, Wilson Bombe. "Bundles in the category of Frölicher spaces and symplectic structure." Thesis, 2008. http://hdl.handle.net/10539/5860.

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Bundles and morphisms between bundles are defined in the category of Fr¨olicher spaces (earlier known as the category of smooth spaces, see [2], [5], [9], [6] and [7]). We show that the sections of Fr¨olicher bundles are Fr¨olicher smooth maps and the fibers of Fr¨olicher bundles have a Fr¨olicher structure. We prove in detail that the tangent and cotangent bundles of a n-dimensional pseudomanifold are locally diffeomorphic to the even-dimensional Euclidian canonical F-space R2n. We define a bilinear form on a finite-dimensional pseudomanifold. We show that the symplectic structure on a cotangent bundle in the category of Fr¨olicher spaces exists and is (locally) obtained by the pullback of the canonical symplectic structure of R2n. We define the notion of symplectomorphism between two symplectic pseudomanifolds. We prove that two cotangent bundles of two diffeomorphic finite-dimensional pseudomanifolds are symplectomorphic in the category of Frölicher spaces.

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14

Aguilar, CESAR. "Local controllability of affine distributions." Thesis, 2010. http://hdl.handle.net/1974/5386.

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In this thesis, we develop a feedback-invariant theory of local controllability for affine distributions. We begin by developing an unexplored notion in control theory that we call proper small-time local controllability (PSTLC). The notion of PSTLC is developed for an abstraction of the well-known notion of a control-affine system, which we call an affine system. Associated to every affine system is an affine distribution, an adaptation of the notion of a distribution. Roughly speaking, an affine distribution is PSTLC if the local behaviour of every affine system that locally approximates the affine distribution is locally controllable in the standard sense. We prove that, under a regularity condition, the PSTLC property can be characterized by studying control-affine systems. The main object that we use to study PSTLC is a cone of high-order tangent vectors, or variations, and these are defined using the vector fields of the affine system. To better understand these variations, we study how they depend on the jets of the vector fields by studying the Taylor expansion of a composition of flows. Some connections are made between labeled rooted trees and the coefficients appearing in the Taylor expansion of a composition of flows. Also, a relation between variations and the formal Campbell-Baker-Hausdorff formula is established. After deriving some algebraic properties of variations, we define a variational cone for an affine system and relate it to the local controllability problem. We then study the notion of neutralizable variations and give a method for constructing subspaces of variations. Finally, using the tools developed to study variations, we consider two important classes of systems: driftless and homogeneous systems. For both classes, we are able to characterize the PSTLC property.
Thesis (Ph.D, Mathematics & Statistics) -- Queen's University, 2010-01-11 20:11:45.466

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15

Hasselberger, Hannes. "The existence of infinitely many closed geodesics on a riemannian manifold, containing an isolated prime closed geodesic with maximal index growth." 2012. https://ul.qucosa.de/id/qucosa%3A16551.

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There are two main approaches to solve the problem of finding closed geodesics on a Riemannian manifold M. The variational approach views a closed geodesic as a closed curve which happens to be a geodesic and it looks for critical points of the energy functional, while the dynamical systems approach views a closed geodesic as a geodesic which happens to close up and looks for periodic orbits of the geodesic ow on the unit tangent bundle.

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16

Neumann, Sebastian [Verfasser]. "A decomposition of the moving cone of a projective manifold according to the Harder-Narasimhan filtration of the tangent bundle / vorgelegt von Sebastian Neumann." 2009. http://d-nb.info/1000711099/34.

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17

Bauer, David. "Towards Discretization by Piecewise Pseudoholomorphic Curves." Doctoral thesis, 2012. https://ul.qucosa.de/id/qucosa%3A12277.

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This thesis comprises the study of two moduli spaces of piecewise J-holomorphic curves. The main scheme is to consider a subdivision of the 2-sphere into a collection of small domains and to study collections of J-holomorphic maps into a symplectic manifold. These maps are coupled by Lagrangian boundary conditions. The work can be seen as finding a 2-dimensional analogue of the finite-dimensional path space approximation by piecewise geodesics on a Riemannian manifold (Q,g). For a nice class of target manifolds we consider tangent bundles of Riemannian manifolds and symplectizations of unit tangent bundles. Via polarization they provide a rich set of Lagrangians which can be used to define appropriate boundary value problems for the J-holomorphic pieces. The work focuses on existence theory as a pre-stage to global questions such as combinatorial refinement and the quality of the approximation. The first moduli space of lifted type is defined on a triangulation of the 2-sphere and consists of disks in the tangent bundle whose boundary projects onto geodesic triangles. The second moduli space of punctured type is defined on a circle packing domain and consists of boundary punctured disks in the symplectization of the unit tangent bundle. Their boundary components map into single fibers and at punctures the disks converge to geodesics. The coupling boundary conditions are chosen such that the piecewise problem always is Fredholm of index zero and both moduli spaces only depend on discrete data. For both spaces existence results are established for the J-holomorphic pieces which hold true on a small scale. Each proof employs a version of the implicit function theorem in a different setting. Here the argument for the moduli space of punctured type is more subtle. It rests on a connection to tropical geometry discovered by T. Ekholm for 1-jet spaces. The boundary punctured disks are constructed in the vicinity of explicit Morse flow trees which correspond to the limiting objects under degeneration of the boundary condition.

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