Four-dimensional compact Clifford–Klein forms of pseudo-Riemannian symmetric spaces with signature (2, 2)

We give a classification of reducible and indecomposable pseudo-Riemannian symmetric spaces with signature [Formula: see text] which admit compact Clifford–Klein forms. For this, we develop a method that applies to particular 1-connected solvable symmetric spaces. We also examine a “solvable analogue” of Kobayashi’s conjecture for reductive type and find an evidence that the assumption “reductive type” in the conjecture is crucial.