Math 217a Notes
نویسنده
چکیده
1. Smooth Manifolds: 9/22/14 1 2. Going on a Tangent (Space): 9/24/14 1 3. Immersions and Embeddings: 9/26/14 3 4. Riemannian Metrics: 9/29/14 3 5. Indiana Jones and the Isometries of the Upper Half-Plane: 10/1/14 5 6. That's an Affine Connection You've Got There: 10/3/14 7 7. Missed (Levi-Civita) Connections: 10/6/14 9 8. The Levi-Civita Connection and the Induced Metric: 10/8/14 9 9. Geodesics: 10/10/14 11 10. Geodesics are Locally Minimizing: 10/13/14 13 11. The Gauss Lemma: 10/15/14 14 12. The Hopf-Rinow Theorem: 10/17/14 16 13. Curvature: 10/20/14 17 14. Sectional Curvature: 10/22/14 19 15. The Relation Between Geodesics and Curvature: 10/24/14 21 16. Jacobi Fields Along Geodesics: 10/27/14 22 17. The Cartan-Hadamard Theorem: 10/29/14 24 18. The Path Lifting Property and Covering Maps: 10/31/14 24 19. Theme and Variations: 11/3/14 25 20. The Second Variation of the Energy Functional: 11/5/14 27 21. Weinstein's Theorem: 11/9/14 27 22. The Chern-Weil Theorem and Connections on a Vector Bundle: 11/12/14 28 23. The Fundamental Lemma of Chern-Weil Theory: 11/14/14 30 24. Pontryagin Classes: 11/17/14 32 25. The Pfaffian Form: 11/19/14 33 26. The Pfaffian, Euler Classes, and Chern Classes: 11/21/14 35
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