Differential Geometry II
A selection of the following topics:
● Exponential map and the Hopf-Rinow theorem
● Connection between curvature and topology (e.g. Myer's theorem, Hadamard-Cartan, Klingenberg, rigidity theorems)
● Closed geodesics
● Stokes' theorem and Cohomology
● Spaces of constant curvature, Lie groups, homogeneous spaces
● Conformal geometry, geometric differential equations
● Basic notions from differential topology
(19050)
| Type | Lecture |
|---|---|
| Instructor | Prof. Dr. Konrad Polthier |
| Room | Arnimallee 6 |
| Start | Apr 13, 2015 | 12:00 PM |
| Time | * Lecture: Mo + We, 12 - 14 h, SR 025/026/A6 * Tutorial: We, 16 - 18 h, SR 032/A6 * Exam: 08.07.15: Wed, 12-14h, SR 025/026 * Retake Exam: Mon, 14.09., 12-14h, SR 032/A6 * Post-exam review (retake): Fri, 18.09., 10-11h, R. 208/A6 |
Literature
- Lee, John M., Introduction to Smooth Manifolds, Springer, 2012
- Lee, John M., Riemannian Manifolds: An Introduction to Curvature, Springer, 1997
- Kühnel, Wolfgang, Differentialgeometrie:Kurven - Flächen - Mannigfaltigkeiten, Springer, 2012
- O'Neill, Barret: Semi-Riemannian Geometry with Applications to Relativity, Academic Press, 1983
Further Reading:
- Minimum number of charts for RP^n: http://link.springer.com/chapter/10.1007%2FBFb0085228
- C1-embedding of the flat torus in R^3: http://math.univ-lyon1.fr/~borrelli/Hevea/Presse/index-en.html