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

@article{Pecastaing2018LorentzianMW, title={Lorentzian manifolds with a conformal action of SL(2,R)}, author={Vincent Pecastaing}, journal={Commentarii Mathematici Helvetici}, year={2018} }

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…

## 4 Citations

CONFORMAL ACTIONS OF REAL-RANK 1 SIMPLE LIE GROUPS ON PSEUDO-RIEMANNIAN MANIFOLDS

- MathematicsTransformation Groups
- 2019

Given a simple Lie group G of rank 1, we consider compact pseudo-Riemannian manifolds (M, g) of signature (p, q) on which G can act conformally, and we determine the smallest possible value for the…

Conformal actions of higher rank lattices on compact pseudo-Riemannian manifolds

- MathematicsGeometric and Functional Analysis
- 2020

We investigate conformal actions of cocompact lattices in higher-rank simple Lie groups on compact pseudo-Riemannian manifolds. Our main result gives a general bound on the real-rank of the lattice,…

The conformal group of a compact simply connected Lorentzian manifold

- MathematicsJournal of the American Mathematical Society
- 2021

We prove that the conformal group of a closed, simply connected, real analytic Lorentzian manifold is compact. D'Ambra proved in 1988 that the isometry group of such a manifold is compact. Our result…

Projective and conformal closed manifolds with a higher-rank lattice action.

- Mathematics
- 2019

We prove global results about actions of cocompact lattices in higher-rank simple Lie groups on closed manifolds endowed with either a projective class of connections or a conformal class of…

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