Constant curvature rotational nets and periodic Bäcklund transforms
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866918342883803136 |
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| author | Raujouan, Thomas Rossman, Wayne Suda, Naoya |
| author_facet | Raujouan, Thomas Rossman, Wayne Suda, Naoya |
| contents | After giving explicit parametrizations of discrete constant negative Gaussian curvature surfaces (negative CGC, i.e. discrete pseudospherical surfaces) of revolution, we construct Bäcklund transformations that again will have explicit parametrizations and are new examples of non-rotational discrete pseudospherical surfaces. In the process of doing this, for discrete CGC circular nets, we can provide rotationally invariant families of flat connections and give conditions on them so that the Bäcklund transformations preserve periodicity, that is, have annular topology. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_15408 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Constant curvature rotational nets and periodic Bäcklund transforms Raujouan, Thomas Rossman, Wayne Suda, Naoya Differential Geometry 53A70 (Primary), 53A05 (Secondary) After giving explicit parametrizations of discrete constant negative Gaussian curvature surfaces (negative CGC, i.e. discrete pseudospherical surfaces) of revolution, we construct Bäcklund transformations that again will have explicit parametrizations and are new examples of non-rotational discrete pseudospherical surfaces. In the process of doing this, for discrete CGC circular nets, we can provide rotationally invariant families of flat connections and give conditions on them so that the Bäcklund transformations preserve periodicity, that is, have annular topology. |
| title | Constant curvature rotational nets and periodic Bäcklund transforms |
| topic | Differential Geometry 53A70 (Primary), 53A05 (Secondary) |
| url | https://arxiv.org/abs/2602.15408 |