Content: digest of the following topics:

• exponential map and Hopf-Rinow theorem
• Riemannian manifolds and metrics, Riemannian curvature tensor
• Levi-Civita connection
• connections between curvature und topology (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, numerical application

Literature: will be announced in the lecture.

Actual infromation can be found on the course webpage of the working group:

http://www.mi.fu-berlin.de/en/math/groups/ag-geom/teaching/18_SoSe/DifferentialGeometryII/index.html

• M. Hirsch: Differential topology
• W. Boothby: An Introduction to Differentiable Manifolds and Riemannian Geometry
• J. Lee: Introduction to Smooth Manifolds