Classification of translation surfaces in $\mathbb{R}^3$ with constant sectional curvature
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866907905852178432 |
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| author | Aydin, Muhittin Evren López, Rafael Mihai, Adela |
| author_facet | Aydin, Muhittin Evren López, Rafael Mihai, Adela |
| contents | In this paper, we study translation surfaces in the Euclidean space endowed with a canonical semi-symmetric non-metric connection. We completely classify the translation surfaces of constant sectional curvature with respect to this connection, proving that they are generalized cylinders. This consequence is the same as in the case of the Levi-Civita connection, but in this new setting, there are also generalized cylinders whose sectional curvature can be constant or non-constant, in contrast to the Levi-Civita connection, where the Gaussian curvature is zero. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_12825 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Classification of translation surfaces in $\mathbb{R}^3$ with constant sectional curvature Aydin, Muhittin Evren López, Rafael Mihai, Adela Differential Geometry 53B40, 53C42, 53B20 In this paper, we study translation surfaces in the Euclidean space endowed with a canonical semi-symmetric non-metric connection. We completely classify the translation surfaces of constant sectional curvature with respect to this connection, proving that they are generalized cylinders. This consequence is the same as in the case of the Levi-Civita connection, but in this new setting, there are also generalized cylinders whose sectional curvature can be constant or non-constant, in contrast to the Levi-Civita connection, where the Gaussian curvature is zero. |
| title | Classification of translation surfaces in $\mathbb{R}^3$ with constant sectional curvature |
| topic | Differential Geometry 53B40, 53C42, 53B20 |
| url | https://arxiv.org/abs/2405.12825 |