Monday 11:15 – 12:45, SG 3-12 (Seminargebäude)
Tuesday 9:15 -- 10:45, SG 3-14
First lecture: April, 7
Students:
- Students in mathematics (Diplom)
- students in mathematical physics (M.Sc.)
It is a compulsary elective course in the mathematical physics program (10-MAT-MPDG1)
formed by this lecture and the seminar
Topics:
After a crash course about concepts of differential geometry (connection, geodesics,
parallel transport and curvature),we investigate Riemannian manifolds.
We will discuss how curvature determines topology. In addition we will study
differential operators on Riemannian manifolds,in particular the Laplace-operator.
References:
- Gallot, Hulin, Lafontaine: Riemannian Geometry, 3rd ed., Springer 2004
- Jost: Riemannian Geometry and Geometric Analysis, 7th ed., Springer 2017
- Lee: Riemannian manifolds, An introdution to curvature, GTM 176, Springer 1997
- Petersen: Riemannian Geometry, 3rd ed., Springer 2016
Online Material:
- Bär, Differential Geometry, https://www.math.uni-potsdam.de/fileadmin/user_upload/Prof-Geometrie/Dokumente/Lehre/Lehrmaterialien/DiffGeo.pdf
- Trainer/in: Hans-Bert Rademacher
Semester: ST 2025