Hypersurfaces of non-negative Ricci curvature in a Euclidean space
type: Item
instance of: scholarly article
title: Hypersurfaces of non-negative Ricci curvature in a Euclidean space
zbMATH Open document ID: 0762.53003
DOI: 10.1007/BF01225765
author: Sharief Deshmukh
published in: Journal of Geometry
publication date: 1993-01-17T00:00:00Z
review text: Let \(M\) be a compact and connected hypersurface in a Euclidean space \(\mathbb{R}^{n+1}\) with the position vector field \(x\). It is proved that if the Ricci curvature of \(M\) is non-negative and the scalar curvature \(S\) of \(M\) satisfies \(\| x\|^ 2 S\leq n(n-1)\), then \(M\) is an imbedded sphere.
reviewed by: Ülo Lumiste
Mathematics Subject Classification ID: 53A07
zbMATH DE Number: 98728
zbMATH Keywords: Ricci curvature
zbMATH Keywords: scalar curvature
zbMATH Keywords: sphere
MaRDI profile type: Publication
cites work: Q5565587
description: scientific article; zbMATH DE number 98728