Department of Mathematics

Differential Geometry II

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Prerequisites: Manifolds and tangent bundles as taught e.g. in the Differential Geometry I course during the fall semester 2015.

Contents: In this course, we will define Riemannian metrics on smooth manifolds and use them to study geodesics. We also study derivates of vector fields with respect to each other, leading to the notion of connection. In general, there are many possible connections. However, on a Riemannian manifold there is a preferred one, the Levi-Civita connection. Using the framework of connections we will extremely efficiently identify geodesics as curves whose acceleration vanishes. After introducing various notions of curvature we move on to the relation between local curvature properties of a Riemannian manifold and its global properties, e.g. properties of its fundamental group or de Rham cohomology spaces.

Lecturer: Prof. Dr. Marc Burger
Organizer: Stephan Tornier


On Mondays: 1-3 p.m. at HG D 3.2, starting on February 22.
On Wednesdays: 1-3 p.m. at HG E 1.2.


According to the following table, starting on February 26.

Assistants Time Place Box
Franziska Borer , Berit Singer , Micha Wasem Fridays, 9-10 a.m. HG E 1.1 HG F 28
Franziska Borer , Berit Singer , Micha Wasem Fridays, 10-11 a.m. HG E 1.1 HG F 28
Franziska Borer , Berit Singer , Micha Wasem Fridays, 12-1 p.m. HG E 1.1 HG F 28

Exercise Sheets


The following items may be useful. As the course progesses lecture notes will be updated here.

M. Berger, A panoramic view of Riemannian Geometry, Springer, 2012.
M. Bridson and A. Haefliger, Metric Spaces of Non-Positive Curvature, Springer, 1999.
M. Burger and S. Tornier, Differential Geometry.
M. Burger and S. Tornier, Riemannian Geometry.
M. P. do Carmo, Riemannian Geometry, Birkhäuser, 1992.
S. Gallot, D. Hulin, J. Lafontaine, Riemannian Geometry, Springer, 2004.


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