Differential geometry : bundles, connections, metrics and curvature /
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 an...
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| Format: | Book |
| Language: | English |
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Oxford ; New York :
Oxford University Press,
[2011]
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| Series: | Oxford mathematics.
Oxford graduate texts in mathematics ; 23. |
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Table of 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.