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

TL;DR

This paper classifies four-dimensional indecomposable pseudo-Riemannian symmetric spaces with signature (2,2), analyzing their models, isometry groups, and the existence of compact quotients, thereby completing prior research in the area.

Contribution

It provides a complete classification of these symmetric spaces, including models, isometry groups, and conditions for compact quotients, advancing understanding of their geometric structure.

Findings

Classification of all such symmetric spaces

Explicit models and isometry groups identified

Conditions for existence of compact quotients determined

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.