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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 ${f}^{\text{'}\text{'}}\le 0$ and $\text{Ric}>\left(n-1\right)\left(f{f}^{\text{'}\text{'}}-{f}^{\text{'}}{}^{2}\right)$ are imposed to solve a Bernstein-type problem.

MSC:
 53C42 Immersions (differential geometry) 53C50 Lorentz manifolds, manifolds with indefinite metrics
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