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| Format: | Preprint |
| Veröffentlicht: |
2024
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| Online-Zugang: | https://arxiv.org/abs/2405.12831 |
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| _version_ | 1866910454544072704 |
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| author | Aydin, Muhittin Evren López, Rafael Mihai, Adela |
| author_facet | Aydin, Muhittin Evren López, Rafael Mihai, Adela |
| contents | Consider the Euclidean space $\mathbb{R}^3$ endowed with a canonical semi-symmetric non-metric connection determined by a vector field $\mathsf{C}\in\mathfrak{X}(\mathbb{R}^3)$. We study surfaces when the sectional curvature with respect to this connection is constant. In case that the surface is cylindrical, we obtain full classification when the rulings are orthogonal or parallel to $\mathsf{C}$. If the surface is rotational, we prove that the rotation axis is parallel to $\mathsf{C}$ and we classify all conical rotational surfaces with constant sectional curvature. Finally, for the particular case $\frac12$ of the sectional curvature, the existence of rotational surfaces orthogonally intersecting the rotation axis is also obtained. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_12831 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Constant sectional curvature surfaces with a semi-symmetric non-metric connection Aydin, Muhittin Evren López, Rafael Mihai, Adela Differential Geometry 53B40, 53C42, 53B20 Consider the Euclidean space $\mathbb{R}^3$ endowed with a canonical semi-symmetric non-metric connection determined by a vector field $\mathsf{C}\in\mathfrak{X}(\mathbb{R}^3)$. We study surfaces when the sectional curvature with respect to this connection is constant. In case that the surface is cylindrical, we obtain full classification when the rulings are orthogonal or parallel to $\mathsf{C}$. If the surface is rotational, we prove that the rotation axis is parallel to $\mathsf{C}$ and we classify all conical rotational surfaces with constant sectional curvature. Finally, for the particular case $\frac12$ of the sectional curvature, the existence of rotational surfaces orthogonally intersecting the rotation axis is also obtained. |
| title | Constant sectional curvature surfaces with a semi-symmetric non-metric connection |
| topic | Differential Geometry 53B40, 53C42, 53B20 |
| url | https://arxiv.org/abs/2405.12831 |