Relevant bibliographies by topics / Fiber bundles (Mathematics) Geometry, Differential

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Academic literature on the topic 'Fiber bundles (Mathematics) Geometry, Differential'

Author: Grafiati
Published: 4 June 2021
Last updated: 1 February 2022

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Journal articles on the topic "Fiber bundles (Mathematics) Geometry, Differential"

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del Hoyo, Matias, and Cristian Ortiz. "Morita Equivalences of Vector Bundles." International Mathematics Research Notices 2020, no. 14 (2018): 4395–432. http://dx.doi.org/10.1093/imrn/rny149.

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Abstract We study vector bundles over Lie groupoids, known as VB-groupoids, and their induced geometric objects over differentiable stacks. We establish a fundamental theorem that characterizes VB-Morita maps in terms of fiber and basic data, and use it to prove the Morita invariance of VB-cohomology, with implications to deformation cohomology of Lie groupoids and of classic geometries. We discuss applications of our theory to Poisson geometry, providing a new insight over Marsden–Weinstein reduction and the integration of Dirac structures. We conclude by proving that the derived category of VB-groupoids is a Morita invariant, which leads to a notion of VB-stacks, and solves (an instance of) an open question on representations up to homotopy.
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MacKenzie, K. C. H. "DIFFERENTIAL GEOMETRY OF FRAME BUNDLES." Bulletin of the London Mathematical Society 22, no. 3 (1990): 311–12. http://dx.doi.org/10.1112/blms/22.3.311.

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Nishimura, Hirokazu. "Synthetic differential geometry of jet bundles." Bulletin of the Belgian Mathematical Society - Simon Stevin 8, no. 4 (2001): 639–50. http://dx.doi.org/10.36045/bbms/1102714793.

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Donaldson, S. "DIFFERENTIAL GEOMETRY OF COMPLEX VECTOR BUNDLES." Bulletin of the London Mathematical Society 21, no. 1 (1989): 104–6. http://dx.doi.org/10.1112/blms/21.1.104.

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Okonek, Christian. "Book Review: Differential geometry of complex vector bundles." Bulletin of the American Mathematical Society 19, no. 2 (1988): 528–31. http://dx.doi.org/10.1090/s0273-0979-1988-15731-x.

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Nishimura, H. "Corrigenda to: "Synthetic differential geometry of jet bundles''." Bulletin of the Belgian Mathematical Society - Simon Stevin 9, no. 3 (2002): 473. http://dx.doi.org/10.36045/bbms/1102715071.

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Donaldson, Simon. "Atiyah’s work on holomorphic vector bundles and gauge theories." Bulletin of the American Mathematical Society 58, no. 4 (2021): 567–610. http://dx.doi.org/10.1090/bull/1748.

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The first part of the article surveys Atiyah’s work in algebraic geometry during the 1950s, mainly on holomorphic vector bundles over curves. In the second part we discuss his work from the late 1970s on mathematical aspects of gauge theories, involving differential geometry, algebraic geometry, and topology.
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CRAMPIN, M., and D. J. SAUNDERS. "Fefferman-type metrics and the projective geometry of sprays in two dimensions." Mathematical Proceedings of the Cambridge Philosophical Society 142, no. 3 (2007): 509–23. http://dx.doi.org/10.1017/s0305004107000047.

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AbstractA spray is a second-order differential equation field on the slit tangent bundle of a differentiable manifold, which is homogeneous of degree 1 in the fibre coordinates in an appropriate sense; two sprays which are projectively equivalent have the same base-integral curves up to reparametrization. We show how, when the base manifold is two-dimensional, to construct from any projective equivalence class of sprays a conformal class of metrics on a four-dimensional manifold, of signature (2, 2); the Weyl conformal curvature of these metrics is simply related to the projective curvature of the sprays, and the geodesics of the sprays determine null geodesics of the metrics. The metrics in question have previously been obtained by Nurowski and Sparling (Classical and Quantum Gravity20 (2003) 4995–5016), by a different method involving the exploitation of a close analogy between the Cartan geometry of second-order ordinary differential equations and of three-dimensional Cauchy–Riemann structures. From this perspective the derived metrics are seen to be analoguous to those defined by Fefferman in the CR theory, and are therefore said to be of Fefferman type. Our version of the construction reveals that the Fefferman-type metrics are derivable from the scalar triple product, both directly in the flat case (which we discuss in some detail) and by a simple extension in general. There is accordingly in our formulation a very simple expression for a representative metric of the class in suitable coordinates.
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Kupferman, Raz, Elihu Olami, and Reuven Segev. "Stress theory for classical fields." Mathematics and Mechanics of Solids 25, no. 7 (2017): 1472–503. http://dx.doi.org/10.1177/1081286517723697.

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Classical field theories, together with the Lagrangian and Eulerian approaches to continuum mechanics, are embraced under a geometric setting of a fiber bundle. The base manifold can be either the body manifold of continuum mechanics, the space manifold, or space–time. Differentiable sections of the fiber bundle represent configurations of the system and the configuration space containing them is given the structure of an infinite-dimensional manifold. Elements of the cotangent bundle of the configuration space are interpreted as generalized forces and a representation theorem implies that there exists a stress object representing forces, non-uniquely. The properties of stresses are studied, as well as the role of constitutive relations in this general setting.
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BRANSON, THOMAS, and OUSSAMA HIJAZI. "IMPROVED FORMS OF SOME VANISHING THEOREMS IN RIEMANNIAN SPIN GEOMETRY." International Journal of Mathematics 11, no. 03 (2000): 291–304. http://dx.doi.org/10.1142/s0129167x00000165.

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We improve the hypotheses on some vanishing theorems for first order differential operators on bundles over a Riemannian spin manifold. The improved hypotheses are uniform, in the sense that they are the same for each of an infinite sequence of bundles in each even dimension. They are also elementary, in the sense that they involve only the bottom eigenvalue of the Yamabe operator on scalars, and the pointwise action of the Weyl conformal curvature tensor on two-forms. In particular, they do not make reference to the higher spin bundles on which the conclusion holds.
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Dissertations / Theses on the topic "Fiber bundles (Mathematics) Geometry, Differential"

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Stelmastchuk, Simão Nicolau 1977. "Martingales no fibrado de bases e seções harmonicas via calculo estocastico." [s.n.], 2007. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306326.

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Orientador: Pedro Jose Catuogno<br>Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica<br>Made available in DSpace on 2018-08-09T00:50:27Z (GMT). No. of bitstreams: 1 Stelmastchuk_SimaoNicolau_D.pdf: 537546 bytes, checksum: f06c81c8cd3b758c84d267af8373abdd (MD5) Previous issue date: 2007<br>Resumo: Neste trabalho estudamos os martingales no fibrado de bases e suas relações com os martingales no fibrado tangente. Caracterizamos as aplicações harmônicas a valores no fibrado de bases e as relacionamos com as aplicações harmônicas a valores no fibrado tangente. Numa segunda parte estudamos a harmonicidade das seções de um fibrado via geometria estocástica. Seja P(M;G) um fibrado principal e E(M;N; G; P) um fibrado associado a P(M;G). Entre outros resultados obtemos que: uma seção s : M - E é harmônica se, e somente se, o seu levantamento eqüivariante Fs : P - N é horizontalmente harmônico; e se a ação à esquerda de G × N em N não fixa pontos então não existe seção s : M - E harmônica ou toda seção harmônica é nula<br>Abstract: Neste trabalho estudamos os martingales no fibrado de bases e suas relações com os martingales no fibrado tangente. Caracterizamos as aplicações harmônicas a valores no fibrado de bases e as relacionamos com as aplicações harmônicas a valores no fibrado tangente. Numa segunda parte estudamos a harmonicidade das seções de um fibrado via geometria estocástica. Seja P(M;G) um fibrado principal e E(M;N; G; P) um fibrado associado a P(M;G). Entre outros resultados obtemos que: uma seção s : M - E é harmônica se, e somente se, o seu levantamento eqüivariante Fs : P - N é horizontalmente harmônico; e se a ação à esquerda de G × N em N não fixa pontos então não existe seção s : M - E harmônica ou toda seção harmônica é nula<br>Doutorado<br>Geometria Estocastica<br>Doutor em Matemática
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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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Kramer, Wolfram. "Der Diracoperator auf Faserungen." Bonn : [s.n.], 1999. http://catalog.hathitrust.org/api/volumes/oclc/41464666.html.

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Genaro, Rafael 1989. "Grupo de holonomia e o teorema de Berger." [s.n.], 2013. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306399.

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Orientador: Rafael de Freitas Leão<br>Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica<br>Made available in DSpace on 2018-08-23T07:15:26Z (GMT). No. of bitstreams: 1 Genaro_Rafael_M.pdf: 1032495 bytes, checksum: 30e0fabb7aa149ab240fc0b3ae0b6d46 (MD5) Previous issue date: 2013<br>Resumo: Dada uma conexão sobre um fibrado vetorial podemos usá-la para construir o transporte paralelo de elementos do fibrado ao longo de curvas da variedade base. Esta operação nos fornece isomorfismos lineares entre as fibras do fibrado em questão, mas quando consideramos laços na variedade base o ponto de partida é igual ao ponto de chegada, desta forma obtemos um isomorfismo da fibra sobre este ponto nela mesma. O conjunto de isomorfismos obtidos por esta construção formam um grupo chamado Grupo de Holonomia. Quando consideramos o fibrado tangente de uma variedade riemanniana com a conexão Levi-Civita o grupo de holonomia está intrinsecamente relacionado com a geometria da variedade. Esta foi explorada por Marcel Berger para classificar quais grupos podem aparecer como holonomia de uma variedade riemanniana. O objetivo desta dissertação é fornecer uma demonstração geométrica, obtida por Carlos Olmos, deste resultado<br>Abstract: Given a connection over a vector bundle we can use it to build the parallel transport of elements in the bundle along curves of the base manifold. This function provides us with linear isomorphisms between the fibers of the bundle in question, but when we consider loops in the base manifold starting point is equal to the arrival point, this way we obtain an isomorphism of the fiber over this point in itself. The set of isomorphism obtained by this construction form a group called Holonomy Group. When we consider the tangent bundle of a Riemannian manifold with Levi-Civita connection the holonomy group is intrinsically related to the geometry of the array. This was explored by Marcel Berger to classify which groups can appear as holonomy of a Riemannian manifold. The objective of this dissertation is to provide a geometric demonstration, obtained by Carlos Olmos, this result<br>Mestrado<br>Matematica<br>Mestre em Matemática
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França, Elizeu Cleber dos Santos 1987. "Soluções invariantes de operadores diferenciais definidos em fibrados." [s.n.], 2014. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306329.

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Orientador: Pedro José Catuogno<br>Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica<br>Made available in DSpace on 2018-08-25T09:06:57Z (GMT). No. of bitstreams: 1 Franca_ElizeuCleberdosSantos_M.pdf: 3490670 bytes, checksum: 6589d1bb5b880e51625fb93abb2964a9 (MD5) Previous issue date: 2014<br>Resumo: Neste trabalho, apresentaremos a teoria básica de simetrias de equações diferenciais, focando na busca por soluções invariantes de operadores diferenciais definidos em fibrados vetoriais com relação a ação transversal de um grupo de Lie no fibrado em questão<br>Abstract: In this work we will give the basic theory of symmetries of differential equations. The goal of this work is searching for invariant solutions of differential operators which are defined on vector bundles with respect to the transverse action of a Lie group in such bundle<br>Mestrado<br>Matematica<br>Mestre em Matemática
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Spinaci, Marco. "Déformations des applications harmoniques tordues." Phd thesis, Grenoble, 2013. http://tel.archives-ouvertes.fr/tel-00877310.

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On étudie les déformations des applications harmoniques $f$ tordues par rapport à une représentation. Après avoir construit une application harmonique tordue "universelle", on donne une construction de toute déformations du premier ordre de $f$ en termes de la théorie de Hodge ; on applique ce résultat à l'espace de modules des représentations réductives d'un groupe de Kähler, pour démontrer que les points critiques de la fonctionnelle de l'énergie $E$ coïncident avec les représentations de monodromie des variations complexes de structures de Hodge. Ensuite, on procède aux déformations du second ordre, où des obstructions surviennent ; on enquête sur l'existence de ces déformations et on donne une méthode pour les construire. En appliquant ce résultat à la fonctionnelle de l'énergie comme ci-dessus, on démontre (pour n'importe quel groupe de présentation finie) que la fonctionnelle de l'énergie est strictement pluri sous-harmonique sur l'espace des modules des représentations. En assumant de plus que le groupe soit de Kähler, on étudie les valeurs propres de la matrice hessienne de $E$ aux points critiques.
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Smith, Benjamin. "The Differential Geometry of Instantons." Thesis, 2009. http://hdl.handle.net/10012/4541.

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The instanton solutions to the Yang-Mills equations have a vast range of practical applications in field theories including gravitation and electro-magnetism. Solutions to Maxwell's equations, for example, are abelian gauge instantons on Minkowski space. Since these discoveries, a generalised theory of instantons has been emerging for manifolds with special holonomy. Beginning with connections and curvature on complex vector bundles, this thesis provides some of the essential background for studying moduli spaces of instantons. Manifolds with exceptional holonomy are special types of seven and eight dimensional manifolds whose holonomy group is contained in G2 and Spin(7), respectively. Focusing on the G2 case, instantons on G2 manifolds are defined to be solutions to an analogue of the four dimensional anti-self-dual equations. These connections are known as Donaldson-Thomas connections and a couple of examples are noted.
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(10724076), Daniel L. Bath. "Bernstein--Sato Ideals and the Logarithmic Data of a Divisor." Thesis, 2021.

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We study a multivariate version of the Bernstein–Sato polynomial, the so-called Bernstein–Sato ideal, associated to an arbitrary factorization of an analytic germ <i>f - f</i><sub>1</sub>···<i>f</i><sub>r</sub>. We identify a large class of geometrically characterized germs so that the <i>D</i><sub>X,x</sub>[<i>s</i><sub>1</sub>,...,<i>s</i><sub>r</sub>]-annihilator of <i>f</i><sup>s</sup><sub>1</sub><sup>1</sup>···<i>f</i><sup>s</sup><sub>r</sub><sup>r</sup> admits the simplest possible description and, more-over, has a particularly nice associated graded object. As a consequence we are able to verify Budur’s Topological Multivariable Strong Monodromy Conjecture for arbitrary factorizations of tame hyperplane arrangements by showing the zero locus of the associated Bernstein–Sato ideal contains a special hyperplane. By developing ideas of Maisonobe and Narvaez-Macarro, we are able to find many more hyperplanes contained in the zero locus of this Bernstein–Sato ideal. As an example, for reduced, tame hyperplane arrangements we prove the roots of the Bernstein–Sato polynomial contained in [−1,0) are combinatorially determined; for reduced, free hyperplane arrangements we prove the roots of the Bernstein–Sato polynomial are all combinatorially determined. Finally, outside the hyperplane arrangement setting, we prove many results about a certain <i>D</i><sub>X,x</sub>-map ∇<sub><i>A</i></sub> that is expected to characterize the roots of the Bernstein–Sato ideal.
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Books on the topic "Fiber bundles (Mathematics) Geometry, Differential"

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Koszul, J. L. Lectures on fibre bundles and differential geometry. Published for the Tata Institute of Fundamental Research [by] Springer-Verlag, 1986.

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Choquet-Bruhat, Yvonne. Graded bundles and supermanifolds. Bibliopolis, 1989.

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Liegroupoids and Lie algebroids in differential geometry. Cambridge University Press, 1987.

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Mackenzie, K. Lie groupoids and Lie algebroids in differential geometry. Cambridge University Press, 1987.

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Luke, Glenys. Vector Bundles and Their Applications. Springer US, 1998.

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Fatibene, Lorenzo. Natural and gauge natural formalism for classical field theories: A geometric perspective including spinors and gauge theories. Springer Science+Business Media, 2003.

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Benedetti, R. Lectures on hyperbolic geometry. Springer-Verlag, 1992.

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M, Francaviglia, ed. Natural and gauge natural formalism for classical field theories: A geometric perspective including spinors and gauge theories. Kluwer Academic, 2003.

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Cordero, Luis A. Differential Geometry of Frame Bundles. Springer Netherlands, 1988.

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Saunders, D. J. The geometry of jet bundles. Cambridge University Press, 1989.

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Book chapters on the topic "Fiber bundles (Mathematics) Geometry, Differential"

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Chern, Shiing-Shen. "Differential Geometry of Fiber Bundles." In Springer Collected Works in Mathematics. Springer New York, 1989. http://dx.doi.org/10.1007/978-1-4614-9343-3_23.

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Walschap, Gerard. "Fiber Bundles." In Metric Structures in Differential Geometry. Springer New York, 2004. http://dx.doi.org/10.1007/978-0-387-21826-7_2.

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Chern, Shiing-shen. "Differential Geometry of Fiber Bundles." In Selected Papers. Springer New York, 1989. http://dx.doi.org/10.1007/978-1-4612-3546-0_23.

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Kassel, Christian. "Principal Fiber Bundles in Non-commutative Geometry." In Quantization, Geometry and Noncommutative Structures in Mathematics and Physics. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-65427-0_3.

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"MANIFOLDS AND FIBER BUNDLES." In Topics in Mathematical Analysis and Differential Geometry. WORLD SCIENTIFIC, 1998. http://dx.doi.org/10.1142/9789812816948_0006.

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"Calculus on fiber bundles." In Applied Differential Geometry. Cambridge University Press, 1985. http://dx.doi.org/10.1017/cbo9781139171786.011.

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Taubes, Clifford Henry. "Vector bundles with ℂn as fiber." In Differential Geometry. Oxford University Press, 2011. http://dx.doi.org/10.1093/acprof:oso/9780199605880.003.0006.

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"Characteristic Classes of Fibre Bundles." In An Introduction to Differential Geometry and Topology in Mathematical Physics. WORLD SCIENTIFIC, 1999. http://dx.doi.org/10.1142/9789812816016_0010.

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"Fibre Bundles and their Topological Structures." In An Introduction to Differential Geometry and Topology in Mathematical Physics. WORLD SCIENTIFIC, 1999. http://dx.doi.org/10.1142/9789812816016_0008.

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"Connections and Curvatures on Fibre Bundles." In An Introduction to Differential Geometry and Topology in Mathematical Physics. WORLD SCIENTIFIC, 1999. http://dx.doi.org/10.1142/9789812816016_0009.

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