Contact properties of codimension 2 submanifolds with flat normal bundle
type: Item
instance of: scholarly article
title: Contact properties of codimension 2 submanifolds with flat normal bundle
zbMATH Open document ID: 1205.53007
DOI: 10.4171/RMI/617
author: Carmen Romero-Fuster
author: J. J. Nuño-Ballesteros
published in: Revista Matemática Iberoamericana
publication date: 2011-01-10T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.rmi/1282913822
review text: Summary: Given an immersed submanifold \(M^n\subset \mathbb{R}^{n+2}\), we characterize the vanishing of the normal curvature \(R_D\) at a point \(p \in M\) in terms of the behaviour of the asymptotic directions and the curvature locus at \(p\). We relate the affine properties of codimension 2 submanifolds with flat normal bundle with the conformal properties of hypersurfaces in Euclidean space. We also characterize the semiumbilical, hyperspherical and conformally flat submanifolds of codimension 2 in terms of their curvature loci.
Mathematics Subject Classification ID: 53A07
Mathematics Subject Classification ID: 58C25
zbMATH DE Number: 5834478
zbMATH Keywords: asymptotic directions
zbMATH Keywords: \(\nu\)-principal curvature foliation
zbMATH Keywords: umbilicity
zbMATH Keywords: sphericity
zbMATH Keywords: normal curvature
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 5834478