A Characterization of Curves that Lie on a Totally Umbilical Surface of a Space Form
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866917851768553472 |
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| author | López, Rafael |
| author_facet | López, Rafael |
| contents | We give necessary and sufficient conditions on the curvature and the torsion of a regular curve of the space forms $\h^3$ and $\s^3$ to be contained in a totally umbilical surface. In case that the curve has constant torsion, we obtain the value of the curvature of the curve. Also numerical pictures of these curves are shown. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_19501 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Characterization of Curves that Lie on a Totally Umbilical Surface of a Space Form López, Rafael Differential Geometry 53A04, 53A05, 53B20 We give necessary and sufficient conditions on the curvature and the torsion of a regular curve of the space forms $\h^3$ and $\s^3$ to be contained in a totally umbilical surface. In case that the curve has constant torsion, we obtain the value of the curvature of the curve. Also numerical pictures of these curves are shown. |
| title | A Characterization of Curves that Lie on a Totally Umbilical Surface of a Space Form |
| topic | Differential Geometry 53A04, 53A05, 53B20 |
| url | https://arxiv.org/abs/2411.19501 |