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Periodic discrete Darboux transforms

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journal contribution
posted on 2023-11-20, 16:50 authored by J Cho, K Leschke, Y Ogata
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.

Funding

Leverhulme Trust Network Grant IN-2016-019

JSPS Research Fellowships for Young Scientist 21K13799

History

Author affiliation

School of Computing and Mathematical Sciences, University of Leicester

Version

  • VoR (Version of Record)

Published in

Differential Geometry and its Application

Volume

91

Pagination

102065

Publisher

Elsevier BV

issn

0926-2245

Copyright date

2023

Available date

2023-11-20

Language

en

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