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On Lorentz dynamics: From group actions to warped products via homogeneous spaces
Author(s):
A.
Arouche;
M.
Deffaf;
A.
Zeghib
Journal:
Trans. Amer. Math. Soc.
359
(2007),
1253-1263.
MSC (2000):
Primary 53C50, 54H15
Posted:
October 17, 2006
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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.
References:
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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:
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
Posted:
October 17, 2006
Copyright of article:
Copyright
2006,
American Mathematical Society
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