Surfaces with constant Chebyshev angle
type: Item
instance of: scholarly article
title: Surfaces with constant Chebyshev angle
zbMATH Open document ID: 1278.53013
author: Carlos M. C. Riveros
author: Armando M. V. Corro
published in: Tokyo Journal of Mathematics
publication date: 2013-03-19T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.tjm/1358951324
review text: A well-known fact is that one of the most common parameterizations of surfaces with negative Gaussian curvature is the Chebyshev net parameterization in Euclidean 3-space. The angle between the coordinate lines of this parameterization is called Chebyshev angle. The authors of this report characterize these surfaces in terms of a meromorphic function which satisfies a specific differential equation, which is analyzed in detail. An important application (corollary to the main result) associates a four-parameter family of complete surfaces to each constant Chebyshev angle.
reviewed by: Magdalena Daniela Toda
Mathematics Subject Classification ID: 53A10
Mathematics Subject Classification ID: 35C99
zbMATH DE Number: 6146575
zbMATH Keywords: Liouville equation
zbMATH Keywords: Chebyshev net
zbMATH Keywords: asymptotic lines
MaRDI profile type: Publication
OpenAlex ID: W1993838969
cites work: Liouville's formula in arbitrary planar domains
cites work: Uniqueness and globality of the Liouville formula for entire solutions of \(\frac{\partial^2\log\lambda}{\partial z\partial\overline z} + \frac\lambda2=0\)
cites work: Liouville's formula under the viewpoint of minimal surfaces
cites work: Q4296901
cites work: Bianchi surfaces with constant Chebyshev angle
DOI: 10.3836/TJM/1358951324
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description: scientific article; zbMATH DE number 6146575