Affine umbilical surfaces in \(\mathbb{R}^ 4\)
type: Item
instance of: scholarly article
title: Affine umbilical surfaces in \(\mathbb{R}^ 4\)
zbMATH Open document ID: 0852.53014
DOI: 10.1007/BF02567823
author: Christine Scharlach
author: Luc Vrancken
author: M. Magid
published in: Manuscripta Mathematica
publication date: 1996-06-18T00:00:00Z
full work available at URL: https://eudml.org/doc/156128
review text: Consider a surface with codimension 2 in \(\mathbb{R}^4\). There exist different approaches to a theory leading to different canonically determined transversal planes. Here the authors follow an approach of \textit{K. Nomizu} and \textit{L. Vrancken} [Int. J. Math. 4, No. 1, 127-165 (1993; Zbl 0810.53006)]. If for any vector field \(\xi\) in the associated transverse plane the induced Weingarten operator \(S\) is a multiple of the identity operator on the tangent plane, the surface is called affine umbilical. The authors give classifications of subclasses of this class of surfaces.
Mathematics Subject Classification ID: 53A15
zbMATH DE Number: 871768
zbMATH Keywords: affine surfaces
zbMATH Keywords: codimension two
zbMATH Keywords: transversal planes
zbMATH Keywords: Weingarten operator
zbMATH Keywords: affine umbilical
reviewed by: Udo Simon
MaRDI profile type: Publication
cites work: The Affine Mean Curvature Vector for Surfaces in R4
cites work: Zur affinen Differentialgeometrie. I. Über \(p\)-dimensionale Minimalflächen und Sphären im \(n\)-dimensionalen Raum. II. Über zweidimensionale Flächen im vierdimensionalen Raum
cites work: A NEW EQUIAFFINE THEORY FOR SURFACES IN ℝ4
description: scientific article; zbMATH DE number 871768