Introduction to Riemannian Manifolds
Several topics have been added, including an expanded treatment of pseudo-Riemannian metrics, a more detailed treatment of homogeneous spaces and invariant metrics, a completely revamped treatment of comparison theory based on Riccati equations, and a handful of new local-to-global theorems, to name...
| Main Author: | |
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| Format: | eBook |
| Language: | English |
| Published: |
Cham
Springer International Publishing
2018, 2018
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| Edition: | 2nd ed. 2018 |
| Series: | Graduate Texts in Mathematics
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| Subjects: | |
| Online Access: | |
| Collection: | Springer eBooks 2005- - Collection details see MPG.ReNa |
Table of Contents:
- Preface
- 1. What Is Curvature?
- 2. Riemannian Metrics
- 3. Model Riemannian Manifolds
- 4. Connections
- 5. The Levi-Cevita Connection
- 6. Geodesics and Distance
- 7. Curvature
- 8. Riemannian Submanifolds
- 9. The Gauss–Bonnet Theorem
- 10. Jacobi Fields
- 11. Comparison Theory
- 12. Curvature and Topology
- Appendix A: Review of Smooth Manifolds
- Appendix B: Review of Tensors
- Appendix C: Review of Lie Groups
- References
- Notation Index
- Subject Index