Pseudo-Conformal Actions of the M{ö}bius Group

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