Most important examples of null hypersurfaces in a Lorentzian manifold admit an integrable screen distribution, which determines a spacelike foliation of the null hypersurface. In this paper, we obtain conditions for a codimension two spacelike submanifold contained in a null hypersurface to be a leaf of the (integrable) screen distribution. For this, we use the rigging technique to endow the null hypersurface with a Riemannian metric, which allows us to apply the classical Eschenburg maximum principle. We apply the obtained results to classical examples as generalized Robertson–Walker spaces and Kruskal space.

中文翻译：

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通过一个Lorentzian流形中的一个零超曲面来余维两个空间子流形。

洛伦兹流形中零超曲面的最重要示例承认可积的屏幕分布，该分布确定了零超曲面的空间状叶状。在本文中，我们获得了一个条件，其中一个零超曲面中包含的两个维子空间流形是（可积）屏幕分布的叶子。为此，我们使用装配技术为零超曲面赋予了黎曼度量，这使我们可以应用经典的Eschenburg最大原理。我们将获得的结果应用到经典实例中，例如广义的Robertson-Walker空间和Kruskal空间。