Local rigidity of certain actions of solvable groups on the boundaries of rank-one symmetric spaces

Mao Okada

doi:10.3934/jmd.2021004

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2021, Volume 17: 111-143. Doi: 10.3934/jmd.2021004

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Local rigidity of certain actions of solvable groups on the boundaries of rank-one symmetric spaces

Mao Okada

Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba Meguro-ku Tokyo 153-8914, Japan

Received: May 22, 2019

Revised: November 15, 2020

Published: March 2021

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Abstract

Let $ G $ be the group of orientation-preserving isometries of a rank-one symmetric space $ X $ of non-compact type. We study local rigidity of certain actions of a solvable subgroup $ \Gamma \subset G $ on the boundary of $ X $, which is diffeomorphic to a sphere. When $ X $ is a quaternionic hyperbolic space or the Cayley hyperplane, the action we constructed is locally rigid.

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Mathematics Subject Classification: Primary: 37C85; Secondary: 53C24, 57S30.

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References

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