Pseudo-Riemannian symmetric spaces of signature (2,2)

Abstract

We study all four-dimensional simply-connected indecomposable non-semisimple pseudo-Riemannian symmetric spaces whose metric has signature (2,2). We present models and compute their isometry groups. We solve the problem of the existence or non-existence of compact quotients by properly acting discrete subgroups of the isometry group. This continues and completes earlier work by Maeta.

moved section on extrinsic symmetric spaces from appendix to main body, corrected proof of Prop. 4.20 (Prop. 3.20 in v1)