Trapezoidal discrete surfaces: geometry and integrability
type: Item
instance of: scholarly article
title: Trapezoidal discrete surfaces: geometry and integrability
zbMATH Open document ID: 0941.53007
DOI: 10.1016/S0393-0440(99)00010-8
author: W. K. Schief
author: B. Konopelchenko
published in: Journal of Geometry and Physics
publication date: 1999-12-20T00:00:00Z
review text: The authors study trapezoidal surfaces, i.e., surfaces composed of trapezoidal quadrilaterals (discrete analogues of surfaces of revolution). They define discrete principal curvatures and prove that the discrete Gauss equation is the discrete Schrödinger equation. In particular, the authors define discrete surfaces of revolution and investigate surfaces of constant Gaussian curvature, their Darboux transforms, and the class of discrete Weingarten surfaces of revolution for which the principal curvatures are proportional.
Mathematics Subject Classification ID: 53A05
Mathematics Subject Classification ID: 37K25
Mathematics Subject Classification ID: 39A12
zbMATH DE Number: 1356230
zbMATH Keywords: trapezoidal discrete surface
zbMATH Keywords: surface of revolution
zbMATH Keywords: principal curvature
zbMATH Keywords: Gauss equation
zbMATH Keywords: discrete Schrödinger equation
zbMATH Keywords: Darboux transform
reviewed by: Vladislav V. Goldberg
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1356230