Rigidity of complete Euclidean hypersurfaces
type: Item
instance of: scholarly article
title: Rigidity of complete Euclidean hypersurfaces
zbMATH Open document ID: 0667.53003
author: Marcos Dajczer
author: Detlef Gromoll
published in: Journal of Differential Geometry
publication date: 1990-01-01T00:00:00Z
review text: A ruled hypersurface \(N^ n\) of the Euclidean space \({\mathbb{R}}^{n+1}\) is called a ruled strip if all rulings are complete Euclidean spaces. The main result of this paper is that any complete hypersurface \(N^ n\) of \({\mathbb{R}}^{n+1}\), \(n\geq 3\), which does not contain an open subset \(L^ 3\times {\mathbb{R}}^{n-3}\) with \(L^ 3\) unbounded admits nondiscrete isometric deformations only along ruled strips. This result extends a theorem of Sacksteder where N is assumed to be compact.
Mathematics Subject Classification ID: 53A07
Mathematics Subject Classification ID: 53C40
zbMATH DE Number: 4092250
zbMATH Keywords: ruled hypersurface
zbMATH Keywords: isometric deformations
zbMATH Keywords: ruled strips
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.4310/jdg/1214444321
OpenAlex ID: W1579059951
Wikidata QID: Q115182260
DOI: 10.4310/JDG/1214444321
description: scientific article; zbMATH DE number 4092250