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.