On conformally flat submanifolds
type: Item
instance of: scholarly article
title: On conformally flat submanifolds
zbMATH Open document ID: 0865.53006
author: Marcos Dajczer
author: Luis A. Florit
published in: Communications in Analysis and Geometry
publication date: 1997-07-14T00:00:00Z
review text: An immersed submanifold \(f: M^n\to\mathbb{R}^{n+p}\) in a standard flat Euclidean space, endowed with the induced metric, is said to be conformally flat if each point has a neighbourhood conformal to \(\mathbb{R}^n\). Around 1919, nonflat conformally flat hypersurfaces (\(p=1\), \(n\geq 4\)) were completely described by E. Cartan as being any envelope of a 1-parameter family of spheres. The authors generate Cartan's and Moore's results for \(p\leq n-3\). The remaining part of the paper is devoted to the local classification of all conformally flat submanifolds in codimension \(p=2\).
reviewed by: Zdeněk Jankovský
Mathematics Subject Classification ID: 53A07
Mathematics Subject Classification ID: 53A30
zbMATH DE Number: 929684
zbMATH Keywords: codimension 2
zbMATH Keywords: Euclidean space
zbMATH Keywords: conformally flat submanifolds
MaRDI profile type: Publication
Wikidata QID: Q124936557
full work available at URL: cag.1996.v4.n2.a3
OpenAlex ID: W4245391389
DOI: 10.4310/CAG.1996.V4.N2.A3
description: scientific article; zbMATH DE number 929684