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

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

2001-04-17

arxiv.org/abs/nlin/0104036v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

19 pages, 2 figures

Scientific paper

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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