250098 SE Seminar (Differential Geometry) (2017S)

Model spaces in semi-Riemannian geometry.

The goal of this seminar is an in-depth study of a number of concrete model spaces in semi-Riemannian geometry. These include hyperquadrics, space-forms (spaces of constant curvature), warped products, and, time permitting, geometries relevant to General Relativity (Schwarzschild, Robertson-Walker, de Sitter, ...). The required methods (semi-Riemannian coverings, isometry groups, etc.) will be covered as the need arises.

The course presupposes basic knowledge on (Semi-)Riemannian geometry, approximately the material covered e.g. in the course 250070 VO Riemannian geometry of the previous fall term, see http://www.mat.univie.ac.at/~stein/teaching/SoSem16/dg.html#rg Also this seminar can be seen as an extension and practical consolidation of the material presented in the above course. In particular it is well suited for (mildly advanced) students of the "geometry and topology" area of studies according to the master curriculum mathematics.