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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Actions of semisimple Lie groups preserving a degenerate Riemannian metric


Authors: E. Bekkara, C. Frances and A. Zeghib
Journal: Trans. Amer. Math. Soc. 362 (2010), 2415-2434
MSC (2010): Primary 53B30, 53C22, 53C50
Published electronically: December 17, 2009
MathSciNet review: 2584605
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Abstract: We prove a rigidity of the lightcone in Minkowski space. It is (essentially) the unique space endowed with a lightlike metric and supporting an isometric nonproper action of a semisimple Lie group.


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Additional Information

E. Bekkara
Affiliation: Department of Mathematics and Information, BP1523, ENSET of Oran, 31000 El M’naouar Oran, Algeria
Email: esmaa.bekkara@gmail.com

C. Frances
Affiliation: Laboratoire de Mathématiques, Université Paris-Sud, 91405 Orsay Cedex, France
Email: charles.frances@math.u-psud.fr

A. Zeghib
Affiliation: CNRS, UMPA, École Normale Supérieure de Lyon, 69364 Lyon Cexex 07, France
Email: zeghib@umpa.ens-lyon.fr

DOI: http://dx.doi.org/10.1090/S0002-9947-09-05030-2
PII: S 0002-9947(09)05030-2
Keywords: Lightlike metric, lightcone, isotropic direction
Received by editor(s): November 26, 2007
Published electronically: December 17, 2009
Additional Notes: The first author was partially supported by the project CMEP 05 MDU 641B of the Tassili program.
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.