Sur le groupe d'automorphismes des géométries paraboliques de rang 1

Abstract

The aim of this article is to prove the following result, which generalizes the Ferrand–Obata theorem, concerning the conformal group of a Riemannian manifold, and the Schoen–Webster theorem about the automorphism group of a strictly pseudo-convex CR structure: let M be a connected manifold endowed with a regular Cartan geometry, modelled on the boundary X = ∂ H K d of the hyperbolic space of dimension d ⩾ 2 over K , K being R , C , H or the octonions O . If the automorphism group of M does not act properly on M, then M is isomorphic, as a Cartan geometry, to X, or X minus a point.