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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


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.
TypeLecture with tutorial
InstructorProf. Dr. Konrad Polthier, Henriette-Sophie Lipschütz
Contact PersonHenriette-Sophie Lipschütz
Credit Points10
StartApr 20, 2022
endJul 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.