A Ferrand-Obata theorem for rank one parabolic geometries

2006/08/22 by Charles Frances, Frances, Charles
Mathematics · #Advanced Operator Algebra Research #Algebraic and Geometric Analysis #Differential Geometry (math.DG) #FOS: Mathematics #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.math/0608537

openalex publication_date 2006/08/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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