On the unification of classical and novel integrable surfaces: I. Differential geometry

W. K. Schief; B. G. Konopelchenko

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arXiv · nlin/0104036

On the unification of classical and novel integrable surfaces: I. Differential geometry

W. K. Schief·B. G. Konopelchenko

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Abstract

A novel class of integrable surfaces is recorded. This class of O surfaces is shown to include and generalize classical surfaces such as isothermic, constant mean curvature, minimal, `linear' Weingarten, Guichard and Petot surfaces and surfaces of constant Gaussian curvature. It is demonstrated that the construction of a Backlund transformation for O surfaces leads in a natural manner to an associated parameter-dependent linear representation. The classical pseudosphere and breather pseudospherical surfaces are generated.

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W. K. Schief, B. G. Konopelchenko. 2001-04-17. On the unification of classical and novel integrable surfaces: I. Differential geometry. https://arxiv.org/abs/nlin/0104036

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