Reference : Lorentzian manifolds with a conformal action of SL(2,R)
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
http://hdl.handle.net/10993/30058
Lorentzian manifolds with a conformal action of SL(2,R)
English
Pecastaing, Vincent mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
2018
Commentarii Mathematici Helvetici
Birkhauser Verlag
98
2
401-439
Yes (verified by ORBilu)
International
0010-2571
1420-8946
Switzerland
[en] Lorentzian geometry ; Conformal geometry ; Dynamics of Lie groups actions
[en] 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 theorem of Frances and Zeghib to some simple Lie groups of real-rank 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.
Researchers
http://hdl.handle.net/10993/30058
10.4171/CMH/439
https://www.ems-ph.org/journals/show_abstract.php?issn=0010-2571&vol=93&iss=2&rank=6

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