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

2020/09/01 by Maeta, Keiichi · 1 citation
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2009.00233

Abstract

We give a classification of irreducible four-dimensional symmetric spaces G/H which admit compact Clifford-Klein forms, where G is the transvection group of G/H. 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 groups and find an evidence that the reductive assumption in Kobayashi's conjecture is crucial.

Cited by

• On completeness of certain locally symmetric pseudo-Riemannian manifolds of signature (2,2)

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