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

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.