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

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

Okada, Mao
Local Rigidity of Certain Actions of Nilpotent-by-Cyclic Groups on the Sphere
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Abstract:
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

$\partial\mathbb{H}_\mathbb{C}^n = S^{2n-1}$ .

Keywords: Group actions, local rigidity, Heisenberg group.

Mathematics Subject Classification (2010): Primary 37C85; Secondary 53C24, 57S30

Mathematical Reviews Number: MR3929518

Received: 2018-02-20

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