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Totally umbilical lightlike hypersurfaces in Robertson-Walker spacetimes. (English) Zbl 1293.53019
Summary: We study the problem of light-like hypersurfaces immersed into Robertson-Walker (RW) space-times, where the screen bundle of the hypersurface has constant higher-order mean curvature. We consider the following question: Under what conditions is the compact light-like hypersurface totally umbilical? Our approach is based on the relationship between the light-like hypersurface with its screen bundle and the Minkowski formulae for the screen bundle.

MSC:
53B25 Local submanifolds
53Z05 Applications of differential geometry to physics
53B30 Local differential geometry of Lorentz metrics, indefinite metrics
53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.)
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