L1-2-type surfaces in 3-dimensional De Sitter and anti De Sitter spaces
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arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| author | García-Martínez, S. Carolina Lucas, Pascual Ramírez-Ospina, H. Fabián |
| author_facet | García-Martínez, S. Carolina Lucas, Pascual Ramírez-Ospina, H. Fabián |
| contents | Let $M$ be an orientable surface immersed in the De Sitter space $S_1^3$ in $R^4_1$ or anti de Sitter space $H_1^3$ in $R^4_2$. In the case that $M$ is of $L_1$-2-type we prove that the following conditions are equivalent to each other: $M$ has a constant principal curvature; $M$ has constant mean curvature; $M$ has constant second mean curvature. As a consequence, we also show that an $L_1$-2-type surface is either an open portion of a standard pseudo-Riemannian product, or a $B$-scroll over a null curve, or else its mean curvature, its Gaussian curvature and its principal curvatures are all non-constant. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_18019 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | L1-2-type surfaces in 3-dimensional De Sitter and anti De Sitter spaces García-Martínez, S. Carolina Lucas, Pascual Ramírez-Ospina, H. Fabián Differential Geometry 53C50, 53B25, 53B30 Let $M$ be an orientable surface immersed in the De Sitter space $S_1^3$ in $R^4_1$ or anti de Sitter space $H_1^3$ in $R^4_2$. In the case that $M$ is of $L_1$-2-type we prove that the following conditions are equivalent to each other: $M$ has a constant principal curvature; $M$ has constant mean curvature; $M$ has constant second mean curvature. As a consequence, we also show that an $L_1$-2-type surface is either an open portion of a standard pseudo-Riemannian product, or a $B$-scroll over a null curve, or else its mean curvature, its Gaussian curvature and its principal curvatures are all non-constant. |
| title | L1-2-type surfaces in 3-dimensional De Sitter and anti De Sitter spaces |
| topic | Differential Geometry 53C50, 53B25, 53B30 |
| url | https://arxiv.org/abs/2601.18019 |