In the lecture, basic topics in Riemannian Geometry are treated from a theoretical point of view and illustrated with several examples.
Content: digest of the following topics:
- Exponential map and HopfRinow theorem
- Riemannian manifolds and metrics, Riemannian curvature tensor
- LeviCivita connection
- Connections between curvature und topology (e.g. Myers theorem, HadamardCartan theorem, Klingenberg theorem, rigidity theorems)
- Closed geodesics
- Stokes theorem, cohomology
- Spaces of constant curvature, Lie groups, symmetric and homogeneous spaces
- Discretization and numerical application
Literature: will be announced in the lecture.