Screw motion surfaces of constant mean curvature in homogeneous 3-manifolds
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arXiv
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866909436265627648 |
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| author | Käse, Philipp |
| author_facet | Käse, Philipp |
| contents | We study the geometry of non-minimal surfaces of supercritical constant mean curvature invariant under screw motions in the homogeneous 3-manifolds $\mathbb{E}(κ,τ)$ including the space-forms of non-negative curvature. We give a complete classification, thereby unifying and extending various previous results. We give the first classification for the Berger sphere case, and we exhibit a new family of screw motion CMC surfaces, called tubes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2203_10968 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Screw motion surfaces of constant mean curvature in homogeneous 3-manifolds Käse, Philipp Differential Geometry 53A10 (Primary) 53C30, 53C42 (Secondary) We study the geometry of non-minimal surfaces of supercritical constant mean curvature invariant under screw motions in the homogeneous 3-manifolds $\mathbb{E}(κ,τ)$ including the space-forms of non-negative curvature. We give a complete classification, thereby unifying and extending various previous results. We give the first classification for the Berger sphere case, and we exhibit a new family of screw motion CMC surfaces, called tubes. |
| title | Screw motion surfaces of constant mean curvature in homogeneous 3-manifolds |
| topic | Differential Geometry 53A10 (Primary) 53C30, 53C42 (Secondary) |
| url | https://arxiv.org/abs/2203.10968 |