| Content: |
The topics of this course include:
- Geodesics and their local minimising property
- Metric structure and the Hopf--Rinow theorem
- Jacobi fields, first and second variation
- Cartan--Hadamard theorem
- Bonnet--Myers theorem
- Spaces of constant curvature
- Synge theorem, comparison theorems
- Curvature and the growth of the fundamental group
| Prerequesites: |
Basic knowledge of differential geometry as given in the differential geometry course of the bachelor (manifolds, vector fields, differential forms, vector bundles and connections, Riemannian manifolds, the Levi-Civita connection, curvature). Notes of the introductory course in differential geomtery by D. Lindemann in the Summer Term can be found here
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| Literature: |
Do Carmo, Riemannian Geometry,
Gallot, Hulin, Lafontaine, Riemannian Geometry,
O'Neill, Semi-Riemannian Geometry,
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