Periodic discrete Darboux transforms

Fuente: arXiv
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Hauptverfasser: Cho, Joseph, Leschke, Katrin, Ogata, Yuta
Format: Preprint
Veröffentlicht: 2023
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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