Conformal deformations of submanifolds in codimension two
type: Item
instance of: scholarly article
title: Conformal deformations of submanifolds in codimension two
zbMATH Open document ID: 0955.53010
author: Marcos Dajczer
author: Ruy Tojeiro
published in: Journal of the Mathematical Society of Japan
publication date: 2001-02-27T00:00:00Z
review text: It is shown that a certain conformal rigidity holds for conformal immersions \(M^n\to\mathbb{R}^{n+2}\). More precisely, under the assumption that the dimension of any umbilical subspace does not exceed \(n-5\), two conformal immersions of the same manifold are either conformally congruent (that is, equivalent under a conformal mapping of the ambient space) or both can be isometrically realized as hypersurfaces in two Cartan hypersurfaces \(N^{n+1} \to\mathbb{R}^{n+1}\) which in turn are conformal to one another but nowhere conformally congruent. This improves a conformal rigidity theorem by \textit{M. do Carmo} and the first author [Am. J. Math. 109, 963-985 (1987; Zbl 0631.53043)].
Mathematics Subject Classification ID: 53B25
Mathematics Subject Classification ID: 53A30
Mathematics Subject Classification ID: 53A07
zbMATH DE Number: 1439289
zbMATH Keywords: conformal deformation
zbMATH Keywords: conformal nullity
zbMATH Keywords: conformal rigidity
zbMATH Keywords: conformal immersions
zbMATH Keywords: Cartan hypersurfaces
reviewed by: Wolfgang Kühnel
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2969/jmsj/05210041
OpenAlex ID: W2072842179
DOI: 10.2969/JMSJ/05210041
description: scientific article; zbMATH DE number 1439289