ON THE DEFORMATION SPACE OF CLIFFORD–KLEIN FORMS OF SOME EXPONENTIAL HOMOGENEOUS SPACES

Abstract

Let H be a closed connected subgroup of a connected, simply connected exponential solvable Lie group G. We consider the deformation space [Formula: see text] of a discontinuous subgroup Γ of G for the homogeneous space G/H. When H contains [G, G], we exhibit a description of the space [Formula: see text] which appears to involve GLk(ℝ) as a direct product factor, where k designates the rank of Γ. The moduli space [Formula: see text] is also described. Consequently, we prove in such a setup that the local rigidity property fails to hold globally on [Formula: see text] and that every element of the parameters space is topologically stable.