On the average of the scalar curvature of minimal hypersurfaces of spheres with low stability index
type: Item
instance of: scholarly article
title: On the average of the scalar curvature of minimal hypersurfaces of spheres with low stability index
zbMATH Open document ID: 1076.53074
published in: Illinois Journal of Mathematics
publication date: 2005-02-25T00:00:00Z
review text: This paper deals with minimal hypersurfaces in the sphere with low stability index. Let \(M\subset S^n\) be a non totally geodesic compact minimal hypersurface embedded in the \(n\)-dimensional unit sphere \(S^n\). Denote by \(A\) the second fundamental form of \(M\) in \(S^n\). The author proves that if the stability index of \(M\) is equal to \(n+2\) then the average \(\int_M |A|^2\) of the length square of \(A\) is not larger than \(n-1\), where equality holds if and only if \(M\) is isometric to a Clifford minimal hypersurface. Finally, the author proposes two conjectures.
Mathematics Subject Classification ID: 53C42
Mathematics Subject Classification ID: 53A10
zbMATH DE Number: 2138873
zbMATH Keywords: minimal hypersurface
zbMATH Keywords: scalar curvature
zbMATH Keywords: stability index
author: Oscar M. Perdomo
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 2138873