Deforming discontinuous groups for Heisenberg motion groups

Abstract

We study in this paper the local rigidity proprieties of deformation parameters of the natural action of a discontinuous group [Formula: see text] acting on a homogeneous space [Formula: see text], where [Formula: see text] stands for a closed subgroup of the Heisenberg motion group [Formula: see text]. That is, the parameter space admits a locally rigid (equivalently a strongly locally rigid) point if and only if [Formula: see text] is finite. Moreover, Calabi–Markus’s phenomenon and the question of existence of compact Clifford–Klein forms are also studied.