PSEUDO-CONFORMAL ACTIONS OF THE MÖBIUS GROUP

Abstract

We study compact connected pseudo-Riemannian manifolds $(M,g)$ on which the conformal group $\operatorname{Conf}(M,g)$ acts essentially and transitively. We prove, in particular, that if the non-compact semi-simple part of $\operatorname{Conf}(M,g)$ is the Möbius group, then $(M,g)$ is conformally flat