## Local Rigidity of Certain Actions of Nilpotent-by-Cyclic Groups on the Sphere

J. Math. Sci. Univ. Tokyo
Vol. 26 (2019), No. 1, Page 15-53.

Let $G = SU(n, 1)$, $n \geq 2$ be the orientation-pre-serving isometry group of the complex hyperbolic space $\mathbb{H}_\mathbb{C}^n$ with an Iwasawa decomposition $G = KAN$. We prove local rigidity of a family of certain actions of a subgroup $\Gamma \subset AN$ on the imaginary boundary $\partial\mathbb{H}_\mathbb{C}^n = S^{2n-1}$.