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

Published online by Cambridge University Press:  01 November 2007

LUIS J. ALÍAS  and
A. GERVASIO COLARES
LUIS J. ALÍAS*
Affiliation:
Departamento de Matemáticas, Universidad de Murcia, E-30100 Espinardo, Murcia, Spain. e-mail: ljalias@um.es
A. GERVASIO COLARES*
Affiliation:
Departamento de Matemática, Universidade Federal do Ceará, 60455-760 Fortaleza-Ce, Brazil. e-mail: gcolares@mat.ufc.br
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Abstract

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, essentially, under the so called null 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.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 143 , Issue 3 , November 2007 , pp. 703 - 729
Copyright
Copyright © Cambridge Philosophical Society 2007

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