Complete minimal hypersurfaces in \(S^4(1)\) with constant scalar curvature
type: Item
instance of: scholarly article
title: Complete minimal hypersurfaces in \(S^4(1)\) with constant scalar curvature
zbMATH Open document ID: 0735.53047
author: S. Singh
published in: Osaka Journal of Mathematics
publication date: 1992-06-25T00:00:00Z
review text: \textit{S. S. Chern}, \textit{M. do Carmo} and \textit{S. Kobayashi} [Funct. Anal. Relat. Fields, Conf. Chicago 1968, 59--75 (1970; Zbl 0216.44001)] initiated the study of hypersurfaces \(M\) in \(S^{n+1}(1)\) with \(S\) constant, where \(S\) is the square of the length of the second fundamental form. If \(n=3\), \(M\) closed and \(S>3\), then \textit{C. K. Peng} and \textit{C. L. Terng} proved [Semin. on minimal submanifolds, Ann. Math. Stud. 103, 177--198 (1983; Zbl 0534.53048)] that \(S\geq6\). The author proves that the same holds assuming that \(M\) is complete instead of compact.
Mathematics Subject Classification ID: 53C42
zbMATH DE Number: 7353
zbMATH Keywords: minimal surfaces
zbMATH Keywords: constant length
zbMATH Keywords: length of the second fundamental form
reviewed by: Gudlaugur Thorbergsson
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 7353