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)
Regular participation: at least 85% of participation in the tutorials is needed. Active participation: at least 60% of all possible points that can be earned in the homework assignements are needed.| Type | Lecture |
|---|---|
| Instructor | Prof. Dr. Konrad Polthier, Henriette Lipschütz |
| Language | English |
| Credit Points | 10 |
| Room | Arnimallee 6 |
| Start | Apr 16, 2018 |
| Time | *Lecture: Monday, 12-14, 007/008/A6, Wednesday, 12-14, 007/008/A6 *Tutorials: Friday, 10-12, 032/A6 *Exams: first July, 20th, 2018. Dates will be given on request. second: tba |
| Note | The lectures and the tutorials will be held in English on request. |
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
- Guillemin, Victor and Pollack, Alan: Differential Topology, AMS Chelsea Publishing, 2010
- Hirsch, Morris: Differential Topology, Graduate Texts in Mathematics, Springer, 1997
- Kreck, Matthias: Differential Algebraic Topology, Graduate Studies in Mathematics, Band 110, AMS, 2010
- Munkres, James: Topology, Pearson New International Edition, 2013
Further Reading:
- Minimum number of charts for RP^n: http://link.springer.com/chapter/10.1007%2FBFb0085228