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

Author
Taubes, Clifford, 1954- [Browse]
Format
Book
Language
English
Published/​Created
Oxford : Oxford University Press, 2011.
Description
1 online resource (313 p.)

Details

Subject(s)
Series
Summary note
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.
Notes
Description based upon print version of record.
Bibliographic references
Includes bibliographical references and index.
Source of description
Description based on print version record.
Language note
English
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.
ISBN
0-19-162178-1
OCLC
763156939
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