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, Eric Zimmermann |
Language | English |
Credit Points | 10 |
Start | Apr 16, 2022 | 12:00 PM |
end | Jul 18, 2022 | 02:00 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