Zero mean curvature surfaces in isotropic space with planar curvature lines
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866929557915828224 |
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| author | Cho, Joseph Hara, Masaya |
| author_facet | Cho, Joseph Hara, Masaya |
| contents | We give a comprehensive account of zero mean curvature surfaces in isotropic 3-space with planar curvature lines. After giving a complete classification all such surfaces, we show that they belong to a 1-parameter family of surfaces. We then investigate their relationship to Thomsen-type surfaces in isotropic 3-space, those zero mean curvature surfaces in isotropic 3-space that are also affine minimal. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_18728 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Zero mean curvature surfaces in isotropic space with planar curvature lines Cho, Joseph Hara, Masaya Differential Geometry 53A10 (Primary) 53A15, 53A35, 53B30 (Secondary) We give a comprehensive account of zero mean curvature surfaces in isotropic 3-space with planar curvature lines. After giving a complete classification all such surfaces, we show that they belong to a 1-parameter family of surfaces. We then investigate their relationship to Thomsen-type surfaces in isotropic 3-space, those zero mean curvature surfaces in isotropic 3-space that are also affine minimal. |
| title | Zero mean curvature surfaces in isotropic space with planar curvature lines |
| topic | Differential Geometry 53A10 (Primary) 53A15, 53A35, 53B30 (Secondary) |
| url | https://arxiv.org/abs/2410.18728 |