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

Arouche, A.; Deffaf, M.; Zeghib, A.

doi:10.1090/S0002-9947-06-04279-6

On Lorentz dynamics: From group actions to warped products via homogeneous spaces
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by A. Arouche, M. Deffaf and A. Zeghib PDF

Trans. Amer. Math. Soc. 359 (2007), 1253-1263 Request permission

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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