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Differential geometry : bundles, connections, metrics and curvature / Clifford Henry Taubes.

By: Material type: TextSeries: Oxford mathematics | Oxford graduate texts in mathematics ; 23.Publication details: Oxford ; New York : Oxford University Press, c2011.Description: xiii, 298 p. : ill. ; 24 cmISBN:
  • 9780199605880 (hbk.)
  • 0199605882 (hbk.)
  • 9780199605873 pbk.)
  • 0199605874 (pbk.)
Subject(s): DDC classification:
  • 516.36 22
LOC classification:
  • QA641 .T238 2011
Contents:
1. Smooth manifolds -- 2. Matrices and lie groups -- 3. Introduction to vector bundles -- 4. Algebra of vector bundles -- 5. Maps and vector bundles -- 6. Vector bundles with C[superscript n] as fiber -- 7. Metrics on vector bundles -- 8. Geodesics -- 9. Properties of geodesics -- 10. Principal bundles -- 11. Covariant derivatives and connections -- 12. Covariant derivatives, connections and curvature -- 13. Flat connections and holonomy -- 14. Curvature polynomials and characteristic classes -- 15. Covariant derivatives and metrics -- 16. The Riemann curvature tensor -- 17. Complex manifolds -- 18. Holomorphic submanifolds, holomorphic sections and curvature -- 19. The Hodge star.
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.
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Cover image Item type Current library Home library Collection Shelving location Call number Materials specified Vol info URL Copy number Status Notes Date due Barcode Item holds Item hold queue priority Course reserves
Books Blantyre Branch Library General Collection NFIC 516.36 TAU (Browse shelf(Opens below)) Available 0085064
Books Headquarters Lending Library General Collection NFIC 516.36 TAU (Browse shelf(Opens below)) Available 0085063

Includes bibliographical references and index.

1. Smooth manifolds -- 2. Matrices and lie groups -- 3. Introduction to vector bundles -- 4. Algebra of vector bundles -- 5. Maps and vector bundles -- 6. Vector bundles with C[superscript n] as fiber -- 7. Metrics on vector bundles -- 8. Geodesics -- 9. Properties of geodesics -- 10. Principal bundles -- 11. Covariant derivatives and connections -- 12. Covariant derivatives, connections and curvature -- 13. Flat connections and holonomy -- 14. Curvature polynomials and characteristic classes -- 15. Covariant derivatives and metrics -- 16. The Riemann curvature tensor -- 17. Complex manifolds -- 18. Holomorphic submanifolds, holomorphic sections and curvature -- 19. The Hodge star.

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.

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