In this paper, we deal with marginally outer trapped surfaces (MOTS) immersed in the de Sitter space $$\mathbb {S}_1^{n+2}$$ S 1 n + 2 . In this setting we are able to obtain a Simons formula for the null second fundamental form and under some appropriate constraints on the MOTS, we apply a weak maximum principle in order to guarantee that it must be either a totally geodesic submanifold or isometric to an open piece of an isoparametric submanifold with two distinct principal curvatures one of which is simple. In this last case, supposing that the initial data where the MOTS lying is a totally umbilical spacelike hypersurface of $$\mathbb {S}_1^{n+2}$$ S 1 n + 2 , we conclude that it must be either isometric to a circular cylinder, a hyperbolic cylinder or a Clifford torus.

中文翻译：

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德西特空间中MOTS的分类

在本文中，我们处理浸入 de Sitter 空间 $$\mathbb {S}_1^{n+2}$$ S 1 n + 2 中的边缘外陷陷面 (MOTS)。在这种情况下，我们能够获得零第二基本形式的西蒙斯公式，并且在 MOTS 的一些适当约束下，我们应用弱最大值原理以保证它必须是完全测地子流形或等距开具有两个不同主曲率的等参子流形的一部分，其中一个是简单的。在最后一种情况下，假设 MOTS 所在的初始数据是 $$\mathbb {S}_1^{n+2}$$ S 1 n + 2 的完全脐带状空间超曲面，我们得出结论，它必须是与圆柱、双曲线圆柱或克利福德圆环等距。