Umbilicity of surfaces with orthogonal asymptotic lines in \(\mathbb R^ 4\).
type: Item
instance of: scholarly article
title: Umbilicity of surfaces with orthogonal asymptotic lines in \(\mathbb R^ 4\).
zbMATH Open document ID: 1035.53012
DOI: 10.1016/S0926-2245(02)00068-2
author: Federico Sánchez-Bringas
author: María Del Carmen Romero Fuster
published in: Differential Geometry and its Applications
publication date: 2002-08-14T00:00:00Z
review text: The authors study some properties of surfaces \(M\) in 4-space \(\mathbb{R}^4\) all whose points are umbilic with respect to some normal field. In particular, they show that this condition is equivalent to the orthogonality of the globally defined fields of asymptotic directions. The authors also analyze necessary and sufficient conditions for the hypersphericity of surfaces in 4-space \(\mathbb{R}^4\).
reviewed by: Zdeněk Jankovský
Mathematics Subject Classification ID: 53A07
Mathematics Subject Classification ID: 58K15
zbMATH DE Number: 1780871
zbMATH Keywords: asymptotic direction
zbMATH Keywords: umbilicity
zbMATH Keywords: spherical
zbMATH Keywords: hypersphericity of surfaces
MaRDI profile type: Publication
Wikidata QID: Q115338200
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description: scientific article; zbMATH DE number 1780871