The classification problem for pseudo-Riemannian symmetric spaces

TL;DR

This paper surveys recent progress in classifying pseudo-Riemannian symmetric spaces with non-semisimple transvection groups, an open problem in differential geometry, and discusses related applications.

Contribution

It unifies and explains recent results on the classification of pseudo-Riemannian symmetric spaces with non-semisimple transvection groups, advancing understanding in this open problem.

Findings

Progress on classifying non-semisimple transvection group spaces

Unified presentation of previous research results

Discussion of applications in differential geometry

Abstract

Riemannian and pseudo-Riemannian symmetric spaces with semisimple transvection group are known and classified for a long time. Contrary to that the description of pseudo-Riemannian symmetric spaces with non-semisimple transvection group is an open problem. In the last years some progress on this problem was achieved. In this survey article we want to explain these results and some of their applications. Among other things, the material developed in our previous papers math.DG/0312243, math.DG/0408249, and math.DG/0503220 is presented in a unified way.