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A Ferrand-Obata theorem for rank one parabolic geometries

Charles Frances
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Abstract

The aim of this article is the proof of the following result: Let M be a connected manifold endowed with a regular Cartan geometry modelled on the boundary X of the d-dimensional real (resp. complex, resp. quaternionic, resp. octonionic) hyperbolic space. If the group of automorphisms of M does not act properly on M, then M is geometrically isomorphic to: - X if M is compact. - X minus a point in the other cases.

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Charles Frances. 2006-08-22. A Ferrand-Obata theorem for rank one parabolic geometries. https://arxiv.org/abs/math/0608537

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