A splitting of the local rigidity of Clifford-Klein forms of homogeneous spaces of completely solvable Lie groups

TL;DR

This paper introduces a new splitting approach to analyze the local rigidity of Clifford-Klein forms in homogeneous spaces of completely solvable Lie groups, refining existing results and offering a fresh perspective on Baklouti's conjecture.

Contribution

It proposes a novel vertical-horizontal splitting of local rigidity, enhancing understanding and analysis of rigidity phenomena in these geometric structures.

Findings

Refined existing local rigidity results

Introduced a new splitting approach

Provided insights into Baklouti's conjecture

Abstract

In this article, we discuss the local rigidity of Clifford-Klein forms of homogeneous spaces of 1-connected completely solvable Lie groups. In fact, we introduce a splitting of the local rigidity: vertical rigidity and horizontal rigidity. By using this splitting, we refine some existing results about the local rigidity and introduce a new approach to Baklouti's conjecture about the local rigidity.