Rigidity theorems of Clifford torus
type: Item
instance of: scholarly article
zbMATH Open document ID: 0990.53063
DOI: 10.1590/S0001-37652001000300003
published in: Anais da Academia Brasileira de Ciências
publication date: 2002-08-12T00:00:00Z
Mathematics Subject Classification ID: 53C42
zbMATH DE Number: 1672704
zbMATH Keywords: Clifford torus
author: L. A. M. jun. Sousa
MaRDI profile type: Publication
Wikidata QID: Q125277620
cites work: A characterization of complete Riemannian manifolds minimally immersed in the unit sphere
cites work: Harmonic functions on complete riemannian manifolds
full work available at URL: s0001-37652001000300003
OpenAlex ID: W2065239096
title: Rigidity theorems of Clifford torus
review text: Let \(M\) be a closed minimal hypersurface of constant scalar curvature or of constant Gauss-Kronecker curvature in \(S^{n+1}\). The author proves that if \((n-1)\) principal curvatures have the same sign, then \(M\) is congruent to a Clifford torus \(S^1\left(\sqrt{\frac{1}{n}}\right)\times S^{n-1}\left(\sqrt{\frac{n-1}{n}}\right)\).
reviewed by: Koichi Ogiue
description: scientific article; zbMATH DE number 1672704