Classification of ruled surfaces in Lorentz-Minkowski space that are stationary for the moment of inertia
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| author | Aydin, Muhittin Evren López, Rafael |
| author_facet | Aydin, Muhittin Evren López, Rafael |
| contents | In this paper, we study hypersurfaces in Lorentz-Minkowski space $\mathbb{L}^{n+1}$ that are stationary for the moment of inertia with respect to the origin. After giving examples and applications of the maximum principle, we classify, in $\mathbb{L}^3$, all stationary surfaces that are ruled surfaces. We prove that planes are the only cylindrical stationary surfaces. If the surface is not cylindrical, the classification depends on the causal character of the rulings. In addition, we provide explicit parametrizations of all ruled stationary surfaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_17317 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Classification of ruled surfaces in Lorentz-Minkowski space that are stationary for the moment of inertia Aydin, Muhittin Evren López, Rafael Differential Geometry 53A10, 49K05, 74G65 In this paper, we study hypersurfaces in Lorentz-Minkowski space $\mathbb{L}^{n+1}$ that are stationary for the moment of inertia with respect to the origin. After giving examples and applications of the maximum principle, we classify, in $\mathbb{L}^3$, all stationary surfaces that are ruled surfaces. We prove that planes are the only cylindrical stationary surfaces. If the surface is not cylindrical, the classification depends on the causal character of the rulings. In addition, we provide explicit parametrizations of all ruled stationary surfaces. |
| title | Classification of ruled surfaces in Lorentz-Minkowski space that are stationary for the moment of inertia |
| topic | Differential Geometry 53A10, 49K05, 74G65 |
| url | https://arxiv.org/abs/2508.17317 |