On solvable compact Clifford-Klein forms

TL;DR

This paper proves that certain reductive homogeneous spaces do not admit solvable compact Clifford-Klein forms under specific conditions, extending Benoist's non-existence results to a broader class of spaces.

Contribution

It generalizes Benoist's non-existence theorem to a wider class of homogeneous spaces with specific embeddings of H into G.

Findings

Reductive homogeneous spaces with certain embeddings do not admit solvable compact Clifford-Klein forms.

The results extend non-existence theorems beyond nilpotent cases.

Applicable to spaces with 'very regular' embeddings of H into G.

Abstract

In this article we prove that under certain assumptions, a reductive homogeneous space 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 into G.