Let be a Lie group, and let be a finite group. We show in this article that the space is discrete and—in addition—finite if has finitely many connected components. This means that in the case in which is a discontinuous group for the homogeneous space , where is a closed subgroup of , all the elements of Kobayashi’s parameter space are locally rigid. Equivalently, any Clifford–Klein form of finite fundamental group does not admit nontrivial continuous deformations. As an application, we provide a criterion of local rigidity in the context of compact extensions of .
"A local rigidity theorem for finite actions on Lie groups and application to compact extensions of ." Kyoto J. Math. 59 (3) 607 - 618, September 2019. https://doi.org/10.1215/21562261-2019-0018