Lorentzian manifolds with a conformal action of SL(2,R)
Abstract
We consider conformal actions of simple Lie groups on compact Lorentzian manifolds. Mainly motivated by the Lorentzian version of a conjecture of Lichnerowicz, we establish the alternative: Either the group acts isometrically for some metric in the conformal class, or the manifold is conformally flat  that is, everywhere locally conformally diffeomorphic to Minkowski spacetime. When the group is noncompact and not locally isomorphic to SO(1,n), n>1, we derive global conclusions, extending a theorem of Frances and Zeghib to some simple Lie groups of realrank 1. This result is also a first step towards a classification of the conformal groups of compact Lorentz manifolds, analogous to a classification of their isometry groups due to Adams, Stuck and, independently, Zeghib at the end of the 1990's.
 Publication:

arXiv eprints
 Pub Date:
 September 2016
 arXiv:
 arXiv:1609.00358
 Bibcode:
 2016arXiv160900358P
 Keywords:

 Mathematics  Differential Geometry;
 Mathematics  Dynamical Systems;
 53A30;
 53B30;
 57S20;
 37D40;
 37D25
 EPrint:
 38 pages