On the Deformation Space of Clifford–Klein Forms of Heisenberg Groups

Let H be an arbitrary closed connected subgroup of the connected, simply connected Heisenberg G = H2n+1. We present in this paper a complete description of the deformation space $\mathcal{T}(\Gamma, G,H)$ and the moduli space $\mathcal{M}(\Gamma, G,H)$ of adiscontinuous abelian subgroup Γ of G for the homogeneous space G/H. The topological features of deformations, namely the topological stability, the rigidity, and the local rigidity are also studied.