Math 144 Notes: Riemannian Geometry
نویسنده
چکیده
1. Manifolds: 1/7/14 1 2. Tangent and Cotangent Spaces: 1/9/14 3 3. Vector Fields, One-Forms, and Riemannian Metrics: 1/14/14 6 4. The Lie Bracket and Riemannian Connections: 1/16/14 8 5. Existence and Uniqueness of the Riemannian Connection: 1/21/14 10 6. Tensor Fields, Parallel Transport, and Holonomy: 1/23/14 13 7. The Riemann Curvature Tensor: 1/28/14 15 8. Flatness: 1/30/14 17 9. Symmetries of the Curvature Tensor: 2/4/14 19 10. Traces and Sectional Curvature: 2/6/14 21 11. The Second Bianchi Identity: 2/11/14 23 12. Models of Hyperbolic Space: 2/18/14 25 13. The Variational Theory of Geodesics: 2/20/14 27 14. The Jacobi Field Equation and the Exponential Map: 2/25/14 29 15. Uniqueness of Constant-Curvature Spaces: 2/27/14 30 16. The Hilbert-Einstein Action: 3/4/14 32 17. The Schwarzschild Solution: 3/6/14 35 18. The Maximally Extended Schwarzschild Metric: 3/11/14 35 19. Friedman-Robertson-Walker Spaces: 3/13/14 37
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