Periodic discrete Darboux transforms
Fuente:
arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866913700899717120 |
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| author | Cho, Joseph Leschke, Katrin Ogata, Yuta |
| author_facet | Cho, Joseph Leschke, Katrin Ogata, Yuta |
| contents | We express Darboux transformations of discrete polarised curves as parallel sections of discrete connections in the quaternionic formalism. This immediately leads to the linearisation of the monodromy of the transformation. We also consider the integrable reduction to the case of discrete bicycle correspondence. Applying our method to the case of discrete circles, we obtain closed-form discrete parametrisations of all (closed) Darboux transforms and (closed) bicycle correspondences. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_02649 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Periodic discrete Darboux transforms Cho, Joseph Leschke, Katrin Ogata, Yuta Differential Geometry (2020): 53A70 (Primary) 58J72 (Secondary) We express Darboux transformations of discrete polarised curves as parallel sections of discrete connections in the quaternionic formalism. This immediately leads to the linearisation of the monodromy of the transformation. We also consider the integrable reduction to the case of discrete bicycle correspondence. Applying our method to the case of discrete circles, we obtain closed-form discrete parametrisations of all (closed) Darboux transforms and (closed) bicycle correspondences. |
| title | Periodic discrete Darboux transforms |
| topic | Differential Geometry (2020): 53A70 (Primary) 58J72 (Secondary) |
| url | https://arxiv.org/abs/2307.02649 |