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

Abstract

The main result of this paper is the conformal flatness of real-analytic compact Lorentz manifolds of dimension at least $3$ admitting a conformal essential (i.e. conformal, but not isometric) action of a Lie group locally isomorphic 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. 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.

22 pages, 2 figures

Cited by in corpus (2)

• Lorentzian manifolds with a conformal action of SL(2,R)
• Conformal actions of real-rank 1 simple Lie groups on pseudo-Riemannian manifolds