Remarks on complete deformable hypersurfaces in \(\mathbb{R}^ 4\)
type: Item
instance of: scholarly article
title: Remarks on complete deformable hypersurfaces in \(\mathbb{R}^ 4\)
zbMATH Open document ID: 0812.53004
author: Hiroshi Mori
published in: Journal of Differential Geometry
publication date: 1995-05-09T00:00:00Z
review text: It is shown that, for each pair \(\{k_ 1(u), k_ 2(v)\}\) of smooth functions on \(\mathbb{R}\) with some conditions, there exists a family of complete nonruled deformable hypersurfaces \(M(\lambda, k_ 1, k_ 2)\), \(-1/2 < \lambda < 1/2\), in Euclidean space \(\mathbb{R}^ 4\) with rank \(\rho = 2\) almost everywhere. This is an answer to one of the problems posed by \textit{M. Dajczer} and \textit{D. Gromoll} [J. Differ. Geom. 31, No. 2, 401- 416 (1990; Zbl 0686.53009)].
Mathematics Subject Classification ID: 53A07
zbMATH DE Number: 663764
zbMATH Keywords: nonruled hypersurfaces
zbMATH Keywords: isometric deformations
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.4310/jdg/1214455285
OpenAlex ID: W1516827308
Wikidata QID: Q115179453
DOI: 10.4310/JDG/1214455285
description: scientific article; zbMATH DE number 663764