Isothermic nets with spherical parameter lines from discrete holomorphic maps
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910375783432192 |
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| author | Hoffmann, Tim Szewieczek, Gudrun |
| author_facet | Hoffmann, Tim Szewieczek, Gudrun |
| contents | We prove that all discrete isothermic nets with a family of planar or spherical lines of curvature can be obtained from special discrete holomorphic maps via lifted-folding. This novel approach is a generalization and discretization of a classical method to create planar curvature lines on smooth surfaces. In particular, this technique provides an efficient way to construct discrete isothermic topological tori composed of fundamental pieces from discrete periodic holomorphic maps. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_13476 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Isothermic nets with spherical parameter lines from discrete holomorphic maps Hoffmann, Tim Szewieczek, Gudrun Differential Geometry 53A70 (Primary) 53A31, 53A04, 53C12 (Secondary) We prove that all discrete isothermic nets with a family of planar or spherical lines of curvature can be obtained from special discrete holomorphic maps via lifted-folding. This novel approach is a generalization and discretization of a classical method to create planar curvature lines on smooth surfaces. In particular, this technique provides an efficient way to construct discrete isothermic topological tori composed of fundamental pieces from discrete periodic holomorphic maps. |
| title | Isothermic nets with spherical parameter lines from discrete holomorphic maps |
| topic | Differential Geometry 53A70 (Primary) 53A31, 53A04, 53C12 (Secondary) |
| url | https://arxiv.org/abs/2403.13476 |