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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:
53C50Lorentz manifolds, manifolds with indefinite metrics
53C40Global submanifolds (differential geometry)
83C20Classes of solutions of equations in general relativity