Differential Geometry II
In the lecture, basic topics in Riemannian Geometry are treated from a theoretical point of view and illustrated with several examples.
Content: A digest of the following topics will be presented:
- Exponential map and Hopf-Rinow theorem
- Connections between curvature und topology (e.g. Myers theorem, Hadamard-Cartan theorem, Klingenberg theorem, rigidity theorems)
- Closed geodesics
- Stokes theorem, cohomology
- Spaces of constant curvature, Lie groups, symmetric and homogeneous spaces
- Conformal geometry, geometric evolution equations and differential equations from geometric analysis
- Basic concepts from differential topology
(19214301)
To achieve regular and active participation it is necessary to visit at least 75% of the offered tutorials and to earn at least 60% of the possible points on the exercise sheets.| Type | Lecture with exercise session |
|---|---|
| Instructor | Prof. Dr. Konrad Polthier, Dr. Tillmann Kleiner |
| Language | English |
| Credit Points | 10 |
| Start | Apr 15, 2026 | 10:00 AM |
| end | Jul 18, 2026 | 12:00 PM |
| Time |
|
| Note | Precondition: Differential Geometry I |
Literature
- Wolfgang Kühnel - Differentialgeometrie (English version: Differential Geometry)
- Barrett O'Neill - Semi-Riemannian Geometry
- Peter Petersen - Riemannian Geometry
-
Georg Glaeser, Konrad Polthier - Bilder der Mathematik