Isothermic surfaces in $\E^3$ as soliton surfaces

Jan Cieśliński; Piotr Goldstein; Antoni Sym

doi:10.1016/0375-9601(95)00504-v

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Isothermic surfaces in $\E^3$ as soliton surfaces

Jan Cieśliński·Piotr Goldstein·Antoni Sym

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Abstract

We show that the theory of isothermic surfaces in $\E^3$ -- one of the oldest branches of differential geometry -- can be reformulated within the modern theory of completely integrable (soliton) systems. This enables one to study the geometry of isothermic surfaces in $\E^3$ by means of powerful spectral methods available in the soliton theory. Also the associated non-linear system is interesting in itself since it displays some unconventional soliton features and, physically, could be applied in the theory of infinitesimal deformations of membranes.

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Jan Cieśliński, Piotr Goldstein, Antoni Sym. 1995-07-20. Isothermic surfaces in $\E^3$ as soliton surfaces. https://doi.org/10.1016/0375-9601(95)00504-v

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