Spacelike Submanifolds of Codimension Two with Parallel Mean Curvature Vector Field in Lorentz-Minkowski Spacetime Contained in the Light Cone
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866916871006060544 |
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| author | Palomo, Francisco J. Romero, Alfonso |
| author_facet | Palomo, Francisco J. Romero, Alfonso |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_22566 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Spacelike Submanifolds of Codimension Two with Parallel Mean Curvature Vector Field in Lorentz-Minkowski Spacetime Contained in the Light Cone Palomo, Francisco J. Romero, Alfonso Differential Geometry Primary 53C40, 53C42, 58E15, 58J05. Secondary 53C24, 53C18, 53B20 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. |
| title | Spacelike Submanifolds of Codimension Two with Parallel Mean Curvature Vector Field in Lorentz-Minkowski Spacetime Contained in the Light Cone |
| topic | Differential Geometry Primary 53C40, 53C42, 58E15, 58J05. Secondary 53C24, 53C18, 53B20 |
| url | https://arxiv.org/abs/2507.22566 |