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

 

On Lorentz dynamics: From group actions to warped products via homogeneous spaces


Authors: A. Arouche, M. Deffaf and A. Zeghib
Journal: Trans. Amer. Math. Soc. 359 (2007), 1253-1263
MSC (2000): Primary 53C50, 54H15
Published electronically: October 17, 2006
MathSciNet review: 2262849
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Abstract: We show a geometric rigidity of isometric actions of non-compact (semisimple) Lie groups on Lorentz manifolds. Namely, we show that the manifold has a warped product structure of a Lorentz manifold with constant curvature by a Riemannian manifold.


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Additional Information

A. Arouche
Affiliation: Faculté des Mathématiques, Université des Sciences et de la Technologie Houari Boumediene, BP 32 El’Alia, Bab Ezzouar, Alger, Algeria
Email: arouche@math.usthb.dz

M. Deffaf
Affiliation: Faculté des Mathématiques, Université des Sciences et de la Technologie Houari Boumediene, BP 32 El’Alia, Bab Ezzouar, Alger, Algeria
Email: deffaf1@yahoo.fr

A. Zeghib
Affiliation: CNRS, UMPA, École Normale Supérieure de Lyon, 46, allée d’Italie, 69364 Lyon cedex 07, France
Email: Zeghib@umpa.ens-lyon.fr

DOI: http://dx.doi.org/10.1090/S0002-9947-06-04279-6
PII: S 0002-9947(06)04279-6
Keywords: Lorentz manifolds, warped product, semi-simple transformation groups
Received by editor(s): December 14, 2004
Published electronically: October 17, 2006
Article copyright: © Copyright 2006 American Mathematical Society