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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.

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.)
Full Text: DOI
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