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The main result of this paper is the conformal flatness of real-analyticcompact Lorentz manifolds of dimension at least $3$ admitting a conformalessential (i.e. conformal, but not isometric) action of a Lie group locallyisomorphic to PSL(2,R). It is established by using a general result of M.Gromov on local isometries of real-analytic $A$-rigid geometric structures. Ascorollary, we deduce the same conclusion for conformal essential actions ofconnected semi-simple Lie groups on real-analytic compact Lorentz manifolds.This work is a contribution to the understanding of the Lorentzian version of aquestion asked by A. Lichnerowicz.

Essential conformal actions of PSL(2,R) on real-analytic compact Lorentz manifolds