Uniqueness of spacelike hypersurfaces with constant higher order mean curvature in generalized Robertson-Walker spacetimes

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In this paper we study the problem of uniqueness for spacelike hypersurfaces with constant higher order mean curvature in generalized Robertson-Walker (GRW) spacetimes. In particular, we consider the following question: Under what conditions must a compact spacelike hypersurface with constant higher order mean curvature in a spatially closed GRW spacetime be a spacelike slice? We prove that this happens, esentially, under the so called convergence condition. Our approach is based on the use of the Newton transformations (and their associated differential operators) and the Minkowski formulae for spacelike hypersurfaces.
To appear in the Mathematical Proceedings of the Cambridge Philosophical Society (accepted November 2006)

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Differential Geometry, Mathematical Physics, 53C42, 53B30, 53C50

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http://salesiana.dossiersoluciones.com/handle/123456789/155930

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0709.4352
 http://arxiv.org/abs/0709.4352
 Mathematical Proceedings of the Cambridge Philosophical Society 143 (2007), 703--729
 doi:10.1017/S0305004107000576

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