On the curvature lines of surfaces in a Euclidean space \(E^4\)
type: Item
instance of: scholarly article
zbMATH Open document ID: 1030.53008
publication date: 2001-03-20T00:00:00Z
Mathematics Subject Classification ID: 53A07
zbMATH DE Number: 1580092
zbMATH Keywords: lines of curvature
zbMATH Keywords: minimal surfaces
zbMATH Keywords: Chen-surfaces
author: Bernard Rouxel
MaRDI profile type: Publication
title: On the curvature lines of surfaces in a Euclidean space \(E^4\)
published in: Rendiconti del Seminario Matematico di Messina. Serie II
review text: In this work the lines of curvature of a surface in the Euclidean 4-space \(E^4\) are considered. The author uses the method of the moving frame. After obtaining the corresponding differential equation in a new form he studies various properties of the lines of curvature of special classes of surfaces, among them the surfaces of Chen (i.e. surfaces for which the vector of the mean curvature vanishes), the minimal surfaces and the surfaces whose lines of curvature form an harmonic quadruple of curves. The work is nice and well organized.
reviewed by: Stylianos Stamatakis
description: scientific article