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arXiv · 2507.22566

Spacelike Submanifolds of Codimension Two with Parallel Mean Curvature Vector Field in Lorentz-Minkowski Spacetime Contained in the Light Cone

Francisco J. Palomo·Alfonso Romero
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Abstract

A general integral inequality is established for compact spacelike submanifolds of codimension two in the Lorentz-Minkowski spacetime under the assumption that the mean curvature vector field is parallel. This inequality is then used to derive a rigidity result. Specifically, we obtain a complete characterization of all compact spacelike submanifolds with parallel mean curvature vector field that lie in the light cone of the Lorentz-Minkowski spacetime: they must be totally umbilical spheres contained in a spacelike hyperplane in Lorentz-Minkowski spacetime.

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Francisco J. Palomo, Alfonso Romero. 2025-07-30. Spacelike Submanifolds of Codimension Two with Parallel Mean Curvature Vector Field in Lorentz-Minkowski Spacetime Contained in the Light Cone. https://arxiv.org/abs/2507.22566

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