Fachbereich Mathematik

Topics in Riemannian Geometry


The course will begin with a short review of the basics of Riemannian manifolds, geodesics, and curvature, but we will mostly focus on such topics as

  • Hopf-Rinow Theorem
  • Jacobi Fields
  • Comparison Theorems
  • The Laplacian on Riemannian Manifolds


The course will be held in English and will consist of one 2-hour lecture Wed. 12:15 - 14:00 in N14.

There will also be an exercise class Mon. 16:15 - 18:00 in C2A17 (starting Mon. Apr. 23) to discuss the problem sets that will be handed out. Please register here for the exercises.

There will be a final exam. The date and requirements to take the exam will be announced in the first few weeks of the lecture.


    • J. M. Lee. Riemannian Manifolds: An Introduction to Curvature. Springer, 1997.
    • M. P. do Carmo. Riemannian Geometry. Birkhauser, 1991.
    • I. Chavel. Riemannian Geometry: A Modern Introduction. Cambridge, 1995.