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

2001/04/17 by W. K. Schief, Schief, W. K., B. G. Konopelchenko +1 · 1 citation
Engineering · Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Differential Geometry (math.DG) #Elasticity and Material Modeling #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Geometric Analysis and Curvature Flows #math.DG #nlin.SI

paper · pdf · doi:10.48550/arxiv.nlin/0104036

19 pages, 2 figures

arxiv created 2001/04/17 · openalex publication_date 2001/04/17 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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