Generalized constant ratio surfaces in \(\mathbb E^3\)
type: Item
instance of: scholarly article
title: Generalized constant ratio surfaces in \(\mathbb E^3\)
zbMATH Open document ID: 1310.53006
author: Yu Fu
author: Marian Ioan Munteanu
published in: Bulletin of the Brazilian Mathematical Society. New Series
publication date: 2014-06-24T00:00:00Z
review text: The constant angle surfaces in the Euclidean 3-space, i.e., oriented surfaces whose normals make a constant angle with some fixed direction, have been intensively studied in the last years. One possible generalization for this topic is to consider surfaces with the property that the angle between the normal and the position vector is constant, these surface are called constant slope surfaces and they were classified by the second author in [``From golden spirals to constant slope surfaces'', J. Math. Phys. 51, No. 7, Article ID 073507 (2010; \url{doi:10.1063/1.3459064})]. A remarkable property of these special surfaces is that the tangential component of the position vector in the tangent plane of the surface is a principal direction. In this work the authors extend the concept of constant slope surfaces by using this property and call them generalized constant ratio surfaces (GCR surfaces) in order to point out the connection with the constant ratio hypersurfaces in the Euclidean \(n\)-space defined by \textit{B.-Y. Chen} in [Soochow J. Math. 27, No. 4, 353--362 (2001; Zbl 1007.53006)]. They obtain interesting results about flat and constant mean curvature GCR surfaces and give some pictures using MATLAB.
Mathematics Subject Classification ID: 53A05
Mathematics Subject Classification ID: 53B25
Mathematics Subject Classification ID: 53C25
zbMATH DE Number: 6307362
zbMATH Keywords: constant slope surface
zbMATH Keywords: canonical principal direction
zbMATH Keywords: constant ratio hypersurface
describes a project that uses: Matlab
MaRDI profile type: Publication
full work available at URL: s00574-014-0041-2
OpenAlex ID: W2051638116
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DOI: 10.1007/S00574-014-0041-2
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description: scientific article; zbMATH DE number 6307362