Ruled Ricci surfaces and curves of constant torsion
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866916644767399936 |
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| author | de Carvalho, Alcides Domingos, Iury Santos, Roney |
| author_facet | de Carvalho, Alcides Domingos, Iury Santos, Roney |
| contents | We show that all non-developable ruled surfaces endowed with Ricci metrics in the three-dimensional Euclidean space may be constructed using curves of constant torsion and its binormal. This allows us to give characterizations of the helicoid as the only surface of this kind that admits a parametrization with plane line of striction, and as the only with constant mean curvature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_04255 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Ruled Ricci surfaces and curves of constant torsion de Carvalho, Alcides Domingos, Iury Santos, Roney Differential Geometry We show that all non-developable ruled surfaces endowed with Ricci metrics in the three-dimensional Euclidean space may be constructed using curves of constant torsion and its binormal. This allows us to give characterizations of the helicoid as the only surface of this kind that admits a parametrization with plane line of striction, and as the only with constant mean curvature. |
| title | Ruled Ricci surfaces and curves of constant torsion |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2405.04255 |