Differential geometry : bundles, connections, metrics and curvature / Clifford Henry Taubes.
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...
| Uniform Title: | Oxford graduate texts in mathematics ;
23. |
|---|---|
| Main Author: | |
| Language: | English |
| Published: |
Oxford :
Oxford University Press,
2011.
|
| Series: | Oxford graduate texts in mathematics ;
23. |
| Subjects: | |
| Physical Description: | xiii, 298 pages : illustrations ; 25 cm. |
| Format: | Book |
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.