On solvable compact Clifford-Klein forms

Abstract

In this article we prove that under certain assumptions, a reductive homogeneous space G / H G/H does not admit a solvable compact Clifford-Klein form. This generalizes the well known non-existence theorem of Benoist for nilpotent Clifford-Klein forms. This generalization works for a particular class of homogeneous spaces determined by “very regular” embeddings of H H into G G .