Abstract
AbstractIsothermic 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.
Funder
Japan Society for the Promotion of Science
Leverhulme Trust
Publisher
Springer Science and Business Media LLC
Subject
Geometry and Topology,Analysis
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