rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Differential geometry
    sub title: bundles, connections, metrics and curvature
  name:
    name part: Taubes, Clifford
    name part: 1954-
    role:
      role term: creator
  type of resource: text
  genre: bibliography
  genre: Electronic books.
  origin info:
    place:
      place term: enk
    place:
      place term: Oxford
    publisher: Oxford University Press
    date issued: 2011
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: remote
    extent: 1 online resource (xiii, 298 pages) : illustrations
  abstract: Bundles, connections, metrics and curvature are the lingua franca of modern differential geometry and theoretical physics. Supplying graduate students in mathematics or theoretical physics with the fundamentals of these objects, this book would suit a one-semester course on the subject of bundles and the associated geometry.
  table of contents: Cover; Contents; 1 Smooth manifolds; 1.1 Smooth manifolds; 1.2 The inverse function theorem and implicit function theorem; 1.3 Submanifolds of R[sup(m)]; 1.4 Submanifolds of manifolds; 1.5 More constructions of manifolds; 1.6 More smooth manifolds: The Grassmannians; Appendix 1.1 How to prove the inverse function and implicit function theorems; Appendix 1.2 Partitions of unity; Additional reading; 2 Matrices and Lie groups; 2.1 The general linear group; 2.2 Lie groups; 2.3 Examples of Lie groups; 2.4 Some complex Lie groups; 2.5 The groups Sl(n; C), U(n) and SU(n).
  table of contents: 2.6 Notation with regards to matrices and differentialsAppendix 2.1 The transition functions for the Grassmannians; Additional reading; 3 Introduction to vector bundles; 3.1 The definition; 3.2 The standard definition; 3.3 The first examples of vector bundles; 3.4 The tangent bundle; 3.5 Tangent bundle examples; 3.6 The cotangent bundle; 3.7 Bundle homomorphisms; 3.8 Sections of vector bundles; 3.9 Sections of TM and T*M; Additional reading; 4 Algebra of vector bundles; 4.1 Subbundles; 4.2 Quotient bundles; 4.3 The dual bundle; 4.4 Bundles of homomorphisms; 4.5 Tensor product bundles.
  table of contents: 4.6 The direct sum4.7 Tensor powers; Additional reading; 5 Maps and vector bundles; 5.1 The pull-back construction; 5.2 Pull-backs and Grassmannians; 5.3 Pull-back of differential forms and push-forward of vector fields; 5.4 Invariant forms and vector fields on Lie groups; 5.5 The exponential map on a matrix group; 5.6 The exponential map and right/left invariance on Gl(n; C) and its subgroups; 5.7 Immersion, submersion and transversality; Additional reading; 6 Vector bundles with C[sup(n)] as fiber; 6.1 Definitions; 6.2 Comparing definitions; 6.3 Examples: The complexification.
  table of contents: 6.4 Complex bundles over surfaces in R[sup(3)]6.5 The tangent bundle to a surface in R[sup(3)]; 6.6 Bundles over 4-dimensional submanifolds in R[sup(5)]; 6.7 Complex bundles over 4-dimensional manifolds; 6.8 Complex Grassmannians; 6.9 The exterior product construction; 6.10 Algebraic operations; 6.11 Pull-back; Additional reading; 7 Metrics on vector bundles; 7.1 Metrics and transition functions for real vector bundles; 7.2 Metrics and transition functions for complex vector bundles; 7.3 Metrics, algebra and maps; 7.4 Metrics on TM; Additional reading; 8 Geodesics.
  table of contents: 8.1 Riemannian metrics and distance8.2 Length minimizing curves; 8.3 The existence of geodesics; 8.4 First examples; 8.5 Geodesics on SO(n); 8.6 Geodesics on U(n) and SU(n); 8.7 Geodesics and matrix groups; Appendix 8.1 The proof of the vector field theorem; Additional reading; 9 Properties of geodesics; 9.1 The maximal extension of a geodesic; 9.2 The exponential map; 9.3 Gaussian coordinates; 9.4 The proof of the geodesic theorem; Additional reading; 10 Principal bundles; 10.1 The definition; 10.2 A cocycle definition; 10.3 Principal bundles constructed from vector bundles.
  target audience: specialized
  note: Clifford Henry Taubes.
  note: Includes bibliographical references and index.
  note: English.
  subject:
    topic: Geometry, Differential
  subject:
    topic: Géométrie différentielle
  subject:
    topic: MATHEMATICS
    topic: Geometry
    topic: General
  subject:
    topic: Geometry, Differential
  classification: QA641 .T3 2011
  classification: 516.36
  related item:
    title info:
      title: Differential Geometry : Bundles, Connections, Metrics and Curvature
    name:
      name part: Taubes, Clifford Henry.
    origin info:
      publisher: Oxford : OUP Oxford, ©2011
  related item:
    title info:
      title: Oxford graduate texts in mathematics ; 23
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  identifier: http://proxy.library.tamu.edu/login
  record info:
    record content source: UAB
    record creation date: 131003
    record change date: 20260318192735.7
    record identifier: in00005710481
    language of cataloging:
      language term: eng