On submanifolds of two manifolds
type: Item
instance of: scholarly article
title: On submanifolds of two manifolds
zbMATH Open document ID: 0799.53071
DOI: 10.1007/BF02572413
author: Marcos Dajczer
author: Ruy Tojeiro
published in: Mathematische Zeitschrift
publication date: 1994-05-10T00:00:00Z
full work available at URL: https://eudml.org/doc/174577
review text: Suppose \(Q_ c^ N\) denotes the \(N\)-dimensional, complete and simply connected Riemannian manifold of constant sectional curvature \(c\). Consider an \(n\)-dimensional Riemannian manifold which admits two isometric immersions \(f: M\to Q^ N_ c\) and \(g: M\to Q_{\tilde c}^{\tilde N}\) with \(c\neq\tilde c\). Under assumptions on codimensions and on the second fundamental forms of \(f\) and \(g\), the authors describe the relation holding between \(f\) and \(g\) on an open dense subset on \(M\). This result is used to obtain a rigidity theorem for minimal immersions and also to generalize a previous theorem of the authors [J. Differ. Geom. 36, No. 1, 1-18 (1992; Zbl 0768.53027)].
Mathematics Subject Classification ID: 53C42
Mathematics Subject Classification ID: 53B25
zbMATH DE Number: 567450
zbMATH Keywords: isometric immersions
zbMATH Keywords: rigidity
zbMATH Keywords: minimal immersions
reviewed by: James Hebda
MaRDI profile type: Publication
cites work: Rigidity of minimal submanifolds in space forms
cites work: Conformal Rigidity
cites work: Rigidity of isometric immersions of higher codimension
cites work: On compositions of isometric immersions
cites work: Substantial Codimension of Submanifolds: Global Results
cites work: Submanifolds of constant positive curvature. I
OpenAlex ID: W1990240658
description: scientific article; zbMATH DE number 567450