<div class="csl-bib-body">
<div class="csl-entry">Cho, J., Leschke, K., & Ogata, Y. (2022). Generalised Bianchi permutability for isothermic surfaces. <i>Annals of Global Analysis and Geometry</i>, <i>61</i>(4), 799–829. https://doi.org/10.1007/s10455-022-09833-5</div>
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dc.identifier.issn
0232-704X
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dc.identifier.uri
http://hdl.handle.net/20.500.12708/142129
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dc.description.abstract
Isothermic surfaces are surfaces which allow a conformal curvature line parametrisation. They form an integrable system, and Darboux transforms of isothermic surfaces obey Bianchi permutability: for two distinct spectral parameters, the corresponding Darboux transforms have a common Darboux transform which can be computed algebraically. In this paper, we discuss two-step Darboux transforms with the same spectral parameter, and show that these are obtained by a Sym-type construction: All two-step Darboux transforms of an isothermic surface are given, without further integration, by parallel sections of the associated family of the isothermic surface, either algebraically or by differentiation against the spectral parameter.
en
dc.description.sponsorship
Fonds zur Förderung der wissenschaftlichen Forschung (FWF)
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dc.language.iso
en
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dc.publisher
Springer
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dc.relation.ispartof
Annals of Global Analysis and Geometry
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dc.rights.uri
http://creativecommons.org/licenses/by/4.0/
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dc.subject
transformation
en
dc.subject
permutability
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dc.subject
isothermic surfaces
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dc.title
Generalised Bianchi permutability for isothermic surfaces