Article (Scientific journals)
Lorentzian manifolds with a conformal action of SL(2,R)
Pecastaing, Vincent
2018In Commentarii Mathematici Helvetici, 98 (2), p. 401-439
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Keywords :
Lorentzian geometry; Conformal geometry; Dynamics of Lie groups actions
Abstract :
[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.
Disciplines :
Mathematics
Author, co-author :
Pecastaing, Vincent ;  University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit
External co-authors :
no
Language :
English
Title :
Lorentzian manifolds with a conformal action of SL(2,R)
Publication date :
2018
Journal title :
Commentarii Mathematici Helvetici
ISSN :
1420-8946
Publisher :
Birkhauser Verlag, Switzerland
Volume :
98
Issue :
2
Pages :
401-439
Peer reviewed :
Peer Reviewed verified by ORBi
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since 09 March 2017

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