Rigidity theorem for hypersurfaces in a unit sphere
type: Item
instance of: scholarly article
title: Rigidity theorem for hypersurfaces in a unit sphere
zbMATH Open document ID: 1110.53050
author: Guoxin Wei
published in: Monatshefte für Mathematik
publication date: 2007-01-26T00:00:00Z
review text: By investigating hypersurfaces \(M^n\) in the unit sphere \(S^{n+1} (1)\) with \(H_k=0\) and with two distinct principal curvatures, the authors provide a characterization of the torus \(S^1(\sqrt{k/n})\times S^{n-1} (\sqrt{(n-k)/n})\). They extend recent results of \textit{O. Perdomo} [Arch. Math. 82, 180--184 (2004; Zbl 1062.53055), \textit{Q. Wang}, Monatsh. Math. 140, No. 2, 163--167 (2003; Zbl 1066.53112), and \textit{T. Otsuki}, Am. J. Math. 92, 145--173 (1970; Zbl 0196.25102)].
reviewed by: Themistocles M. Rassias
Mathematics Subject Classification ID: 53C42
zbMATH DE Number: 5118925
zbMATH Keywords: principal curvatures
zbMATH Keywords: torus
zbMATH Keywords: Gauss equations
zbMATH Keywords: Clifford minimal hypersurface
zbMATH Keywords: submanifold
MaRDI profile type: Publication
full work available at URL: s00605-005-0378-0
OpenAlex ID: W2024159673
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DOI: 10.1007/S00605-005-0378-0
description: scientific article; zbMATH DE number 5118925