Lorentzian manifolds with a conformal action of SL(2,R)

  title={Lorentzian manifolds with a conformal action of SL(2,R)},
  author={Vincent Pecastaing},
  journal={Commentarii Mathematici Helvetici},
  • V. Pecastaing
  • Published 1 September 2016
  • Mathematics
  • Commentarii Mathematici Helvetici
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 space-time. When the group is non-compact and not locally isomorphic to SO(1,n), n>1, we derive global conclusions, extending a… 
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