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Uniqueness of complete spacelike hypersurfaces of constant mean curvature in generalized Robertson-Walker spacetimes. (English) Zbl 0908.53034
In Section 3, the relation between spacelike hypersurfaces and spacelike graphs in generalized Robertson-Walker spacetimes is given, and the conditions under which all these hypersurfaces are compact are studied. Section 4 contains two new integral formulas for compact spacelike hypersurfaces. In Section 5, a new technique to solve the problem: “when is a complete spacelike hypersurface of constant mean curvature in a generalized Robertson-Walker spacetime totally umbilical and a slice?” is introduced. Finally, the natural conditions \(f'' \leq 0\) and \(\text{Ric} > (n - 1) (ff'' - f'{}^2)\) are imposed to solve a Bernstein-type problem.
Reviewer: P.Stavre (Craiova)

53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.)
53C50 Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics
Full Text: DOI
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