Essential conformal structures in Riemannian and Lorentzian geometry

Abstract

This article is devoted to pseudo-Riemannian essential structures, namely the pseudo-Riemannian manifolds, whose conformal group of transformations cannot be reduced to a group of isometries. A celebrated result of M. Obata and J. Ferrand states that for Riemannian manifolds, the only essential structures are the standard sphere, and the Euclidean space. We discuss what this result becomes in higher signature, focusing on the Lorentzian case.