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Compact space-like hypersurfaces in de Sitter space. (English) Zbl 1084.53049

The author considers compact space-like hypersurfaces in the de Sitter spacetime. Several integral formulas are proven, involving higher-order mean curvatures of the hypersurfaces. The results are applied to characterize the case when the respective hypersurfaces are totally umbilical.

MSC:

53C40 Global submanifolds
53C50 Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics
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