Aarhus University Seal / Aarhus Universitets segl

Cartan Geometry

Adam Ehlers Nyholm Thomsen
Lectures for students by students
Friday, 15 February, 2013, at 14:30-15:30, in Aud. D3 (1531-215)
Cartan geometry can be viewed as a common generalisation of Riemannian geometry and homogeneous manifolds, they were called "espaces généralisés" by Élie Cartan. The basic building block is the concept of a Cartan connection which in the Riemannian case consists of the Levi-Civita connection, and the soldering form. Based on the Cartan connection we can define curvature, torsion, holonomy, which turns out to be related to the usual concepts. Furthermore we get such interesting concepts as hamster geometry and the rolling of a homogeneous spaces on our Cartan manifolds.

Prerequisites: Basic knowledge of manifolds and preferably a bit of Riemannian geometry along with basic knowledge of Lie groups.
Contact person: Thomas Schmidt