Local rigidity of certain actions of nilpotent-by-cyclic groups on the sphere

TL;DR

This paper proves local rigidity for specific actions of a subgroup of the isometry group of complex hyperbolic space on its boundary, enhancing understanding of geometric group actions.

Contribution

It establishes local rigidity results for certain nilpotent-by-cyclic group actions on the boundary of complex hyperbolic space, a novel contribution in geometric group theory.

Findings

Proves local rigidity of subgroup actions on the boundary

Identifies conditions under which actions are rigid

Extends rigidity theory to complex hyperbolic geometry

Abstract

Let G = SU(n,1), n >1 be the orientation-preserving isometry group of the complex hyperbolic space with an Iwasawa decomposition G = KAN. We prove local rigidity of a family of certain actions of a subgroup of AN on the imaginary boundary of the complex hyperbolic space.