Surfaces of constant principal-curvatures ratio in isotropic geometry
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866912652457934848 |
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| author | Yorov, Khusrav Skopenkov, Mikhail Pottmann, Helmut |
| author_facet | Yorov, Khusrav Skopenkov, Mikhail Pottmann, Helmut |
| contents | We study surfaces with a constant ratio of principal curvatures in Euclidean and simply isotropic geometries and characterize rotational, channel, ruled, helical, and translational surfaces of this kind under some technical restrictions (the latter two cases only in isotropic geometry). We use the interlacing of various methods of differential geometry, including line geometry and Lie sphere geometry, ordinary differential equations, and elementary algebraic geometry. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_05968 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Surfaces of constant principal-curvatures ratio in isotropic geometry Yorov, Khusrav Skopenkov, Mikhail Pottmann, Helmut Differential Geometry 53A05, 53A10, 53C42 We study surfaces with a constant ratio of principal curvatures in Euclidean and simply isotropic geometries and characterize rotational, channel, ruled, helical, and translational surfaces of this kind under some technical restrictions (the latter two cases only in isotropic geometry). We use the interlacing of various methods of differential geometry, including line geometry and Lie sphere geometry, ordinary differential equations, and elementary algebraic geometry. |
| title | Surfaces of constant principal-curvatures ratio in isotropic geometry |
| topic | Differential Geometry 53A05, 53A10, 53C42 |
| url | https://arxiv.org/abs/2307.05968 |