Local rigidity of homogeoenous actions of parabolic subgroups of rank-one Lie groups

TL;DR

This paper proves the local rigidity of the natural action of the Borel subgroup of SO_+(n,1) on certain cocompact quotients, contributing to the understanding of geometric group actions in rank-one Lie groups.

Contribution

It establishes the local rigidity of Borel subgroup actions on cocompact quotients of SO_+(n,1), a new result in the theory of Lie group actions.

Findings

Proves local rigidity for n > 2

Focuses on Borel subgroup actions

Applicable to cocompact quotients of SO_+(n,1)

Abstract

We show the local rigidity of the natural action of the Borel subgroup of SO_+(n,1) on a cocompact quotient of SO_+(n,1) for n>2.