Compact hypersurfaces with constant scalar curvature and a congruence theorem
type: Item
instance of: scholarly article
title: Compact hypersurfaces with constant scalar curvature and a congruence theorem
zbMATH Open document ID: 0638.53051
author: Antonio Ros
published in: Journal of Differential Geometry
publication date: 1988-01-01T00:00:00Z
review text: Using integral formulas the following main results are shown which generalize classical congruence theorems: a) The sphere is the only compact hypersurface with constant scalar curvature embedded in the Euclidean space. b) Let \(\psi\) : \(M^ n\to {\mathbb{R}}^{n+1}\) be a compact hypersurface embedded in the Euclidean \((n+1)\)-space. Let \(\psi\) ': \(M^ n\to {\mathbb{R}}^{n+m}\) be an isometric immersion. If the mean curvature vector H' of \(\psi\) ' satisfies \(| H'| \leq H\) everywhere (H denoting the mean curvature of \(\psi)\), then \(\psi\) ' differs from \(\psi\) by a rigid motion.
Mathematics Subject Classification ID: 53C40
zbMATH DE Number: 4040766
zbMATH Keywords: integral formulas
zbMATH Keywords: congruence theorems
zbMATH Keywords: constant scalar curvature
zbMATH Keywords: hypersurface
zbMATH Keywords: mean curvature vector
reviewed by: Bernd Wegner
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.4310/jdg/1214441779
OpenAlex ID: W1545407008
Wikidata QID: Q115184014
DOI: 10.4310/JDG/1214441779
description: scientific article; zbMATH DE number 4040766