Conformal essential actions of PSL(2,R) on real-analytic compact Lorentz manifolds

The main result of this paper is the conformal flatness of real-analytic compact
Lorentz manifolds of dimension at least three admitting a conformal essential action of a
Lie group locally isomorphic to PSL(2,R). It is established by using a general result on
local isometries of real-analytic rigid geometric structures. As corollary, we deduce the same
conclusion for conformal essential actions of connected semi-simple Lie groups on real-analytic
compact Lorentz manifolds. This work is a contribution to the understanding of the
Lorentzian version of a question asked by A. Lichnerowicz.