Totally umbilical lightlike hypersurfaces in Robertson-Walker spacetimes.

*(English)*Zbl 1293.53019Summary: 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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\textit{J. Dong} and \textit{X. Liu}, ISRN Geom. 2014, Article ID 974695, 10 p. (2014; Zbl 1293.53019)

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