Geometric contacts of surfaces immersed in \(\mathbb R^n,n\geqslant 5\)
type: Item
instance of: scholarly article
title: Geometric contacts of surfaces immersed in \(\mathbb R^n,n\geqslant 5\)
zbMATH Open document ID: 1176.53015
author: Sueli I. R. Costa
author: S. M. Moraes
author: Carmen Romero-Fuster
published in: Differential Geometry and its Applications
publication date: 2009-06-11T00:00:00Z
review text: The authors study the extrinsic geometry of surfaces immersed in Euclidean space of dimension \(n \geq 5\) by analysing their contacts with different standard geometrical models, such as hyperplanes and hyperspheres. For this purpose they consider the singularities of the distance squared functions and their relation with the behavior of the curvature ellipses at different points on the surface. (The concept of the curvature ellipse of a surface in Euclidean space was first introduced in [\textit{E. B. Wilson} and \textit{C. L. E. Moore}, American Acad. Proc. 52, 269--368 (1916; JFM 46.1133.02)].) The main problem investigated in this paper concerns the generic distribution of the corank two singularities of the distance squared function and of their corresponding focal centers in the focal set of the surface. This leads in a natural way to the concept of umbilical focus and umbilic curvature.
Mathematics Subject Classification ID: 53A07
Mathematics Subject Classification ID: 53B25
Mathematics Subject Classification ID: 53C42
Mathematics Subject Classification ID: 57R70
Mathematics Subject Classification ID: 57R45
zbMATH DE Number: 5564329
zbMATH Keywords: distance-squared functions
zbMATH Keywords: curvature ellipse
zbMATH Keywords: semiumbilics
zbMATH Keywords: focal set
reviewed by: James Hebda
MaRDI profile type: Publication
full work available at URL: j.difgeo.2008.10.020
OpenAlex ID: W2068609787
Wikidata QID: Q115357359
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DOI: 10.1016/J.DIFGEO.2008.10.020
description: scientific article; zbMATH DE number 5564329