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Remarks on the Darboux transform of isothermic surfaces. (English) Zbl 0892.53003
Using quaternionic calculus [see also the supplementary paper by U. Hertrich-Jeromin, ibid., 335-350 (1997; Zbl 0892.53004), reviewed below], the authors study Darboux and Christoffel transforms of isothermic surfaces in Euclidean space and derive a Riccati equation that characterizes all Darboux transforms of a given isothermic surface.

MSC:
53A10Minimal surfaces, surfaces with prescribed mean curvature
37K35Lie-Bäcklund and other transformations