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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 April, 27th, will take place in presence.

Tutorial: Friday, 10-12, 032/A6, the tutorial on April, 22nd, will take place in presence.

Written exams: July, 29th, 2022, 10-12, retake: September, 22nd, 2022, 10-12. If the exam will take place online or in presence will be announced as soon as possible.

The lectures on May, 18th, and May, 25th, as well as the tutorial on May, 20th, will be held purely online.


Precondition: Differential Geometry I


Will be announced in the lecture.