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Uniqueness of spacelike hypersurfaces with constant higher order mean curvature in generalized Robertson-Walker spacetimes. (English) Zbl 1131.53035
The authors study the problem of uniqueness for space-like hypersurfaces with constant higher order mean curvature in generalized Robertson-Walker (GRW) space-times. In particular, they consider the following question: under what conditions must a compact space-like hypersurface with constant higher order mean curvature in a spatially closed GRW space-time be a space-like slice? They prove that this happens, essentially, under the so called null convergence condition. Their approach is based on the use of the Newton transformations and the Minkowski formulae for space-like hypersurfaces.

MSC:
53C50 Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics
53C40 Global submanifolds
83C20 Classes of solutions; algebraically special solutions, metrics with symmetries for problems in general relativity and gravitational theory
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