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

Abstract

In this paper, we discuss local rigidity of Clifford–Klein forms of homogeneous spaces of 1-connected completely solvable Lie groups. We split the property of local rigidity into two conditions: vertical rigidity and horizontal rigidity. By this separation, we discuss local rigidity, in particular, Baklouti’s conjecture.