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

## Exercise sheets

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