The course gives an introduction into the study of smooth manifolds and Riemannian metrics. Riemannian metrics are a fundamental tool in the geometry and topology of manifolds, and they are also of equal importance in mathematical physics and relativity.
We will cover the basic concepts of differentiable manifolds and the properties of Riemannian and Pseudo-Riemannian metrics, the Levi-Civita connection, geodesics and Riemannian curvature. We will also study the geometry of basic examples, such as constant curvature space forms, submanifolds, and Lie groups.
Analytic continuation of holonomy around a path
B. O'Neill, Semi-Riemannian Geometry
S. Gallot - D. Hulot - J. Lafontaine, Riemannian Geometry
I. Chavel, Riemannian Geometry: A modern Introduction
weitere Hinweise in der Vorlesung.
Grundbegriffe der Topologie
Exercise Sheet 01 pdf
Exercise Sheet 02 pdf
Exercise Sheet 03 pdf
Exercise Sheet 04 pdf
Exercise Sheet 05 pdf
Exercise Sheet 06 pdf
Exercise Sheet 07/08 pdf
Exercise Sheet 09 pdf
Exercise Sheet 10 pdf
Exercise Sheet 11 pdf, Solution (18.07.2011) pdf
Exercise Sheet 12 pdf