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
- Riemannian manifolds and metrics, Riemannian curvature tensor
- Levi-Civita connection
- 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
- discretization and numerical application
(19214301)To achieve regular and active participation it is necessary to visit at least 85% of the offered tutorials and to earn at least 60% of the possible points on the exercise sheets.
|Type||Lecture with tutorial|
|Instructor||Prof. Dr. Konrad Polthier, Henriette-Sophie Lipschütz|
|Contact Person||Henriette-Sophie Lipschütz|
|Start||Apr 20, 2022|
|end||Jul 20, 2022|
Lecture: Wednesday, 10-12, and 12-14, 025/026/A6. The lecture on July, 20th, will take place online.
Tutorial: Friday, 10-12, 032/A6.
Written exams: July, 29th, 2022, 10-12, retake: September, 22nd, 2022, 10-12. Both exams will take place online.
Precondition: Differential Geometry I
Will be announced in the lecture.