Essential conformal actions of PSL(2,R) on real-analytic compact Lorentz manifolds
Differential Geometry
2020-05-20 v1
Abstract
The main result of this paper is the conformal flatness of real-analytic compact Lorentz manifolds of dimension at least 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 -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.
Keywords
Cite
@article{arxiv.1510.08812,
title = {Essential conformal actions of PSL(2,R) on real-analytic compact Lorentz manifolds},
author = {Vincent Pecastaing},
journal= {arXiv preprint arXiv:1510.08812},
year = {2020}
}
Comments
22 pages, 2 figures