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Curvature in Mathematics and Physics
Shlomo Sternberg
Table of Contents
| Introduction | |||||||
| 1. Gauss's Theorem Egregium | |||||||
| 2. Rules of Calculus | |||||||
| 3. Connections on the Tangent Bundle | |||||||
| 4. Levi-Civita's Theorem | |||||||
| 5. Bi-invariant Metrics on a Lie Group | |||||||
| 6. Cartan Calculations | |||||||
| 7. Gauss's Lemma | |||||||
| 8. Variational Formulas | |||||||
| 9. The Hopf-Rinow Theorem | |||||||
| 10. Curvature, Distance and Volume | |||||||
| 11.Review of Special Relativity | |||||||
| 12. The Star Operator and Electromagnetism | |||||||
| 13. Preliminaries to the Einstein Equation | |||||||
| 14. Die Grundlagen der Physik | |||||||
| 15. The Frobenius Theorem | |||||||
| 16. Connections on Principal Bundles | |||||||
| 17. Reduction of Principal Bundles | |||||||
| 18. Superconnections | |||||||
| 19. Semi-Riemannian Submersions | |||||||
| Bibliography | |||||||
| Index |