We show how the topological and geometric properties of the family of null hypersurfaces in a Lorentzian manifold are related with the properties of the ambient manifold itself. In particular, we focus in how the presence of global symmetries and curvature conditions restrict the existence of compact null hypersurfaces. We use these results to show the influence on the existence of compact totally umbilic null hypersurfaceswhich are not totally geodesic. Finally we describe the restrictions that they impose in causality theory.

中文翻译：

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洛伦兹流形中的紧凑零超曲面

我们展示了洛伦兹流形中的零超曲面族的拓扑和几何性质如何与环境流形本身的性质相关。特别是，我们关注于整体对称性和曲率条件的存在如何限制紧致零超曲面的存在。我们使用这些结果来显示对不是完全测地的紧凑的完全脐带零超曲面的存在的影响。最后，我们描述了因果关系理论中它们施加的限制。