Lecturer:

Prof. Dr. Urs Lang

Coordinator:

Tommaso Goldhirsch

Time and Location:

Tuesday and Thursday, from 10 to 12. The video will be uploaded one day later on the ETH Video Portal.

Content

Riemannian manifolds, Levi-Civita connection, geodesics, Hopf-Rinow Theorem, curvature, second fundamental form, Riemannian submersions and coverings, Hadamard-Cartan Theorem, triangle and volume comparison, relations between curvature and topology, spaces of Riemannian manifolds.

Exercises

The new exercise sheet will be posted here on Tuesday. You are supposed to have a look at it before the exercise class, so that you can ask questions if you need to. You have until the following Tuesday to send it to your theaching assistant, before 12:15.

Exercise classes

Starting on 14.03.20, the exercise class will be replaced by the publication of hints for the problem sheets. There is a forum for the students to discuss the current exercise sheet and topics from the lecture. You can access the forum here. Follow the instructions on how to create an account in order to access the forum. If you need further clarification regarding a particular exercise or something discussed in class, please make use of the forum provided.

Literature

• U. Lang, Differential Geometry II, Lecture Notes, 16.06.20.
• Manfredo P. do Carmo, Riemannian Geometry, Birkhäuser 1992.
• S. Gallot, D. Hulin, J. Lafontaine, Riemannian Geometry, Springer 2004.
• B. O'Neill, Semi-Riemannian Geometry, With Applications to Relativity, Academic Press 1983.