\(L_{n/2}\)-pinching theorems for submanifolds with parallel mean curvature in a sphere
type: Item
instance of: scholarly article
title: \(L_{n/2}\)-pinching theorems for submanifolds with parallel mean curvature in a sphere
zbMATH Open document ID: 0824.53048
published in: Journal of the Mathematical Society of Japan
publication date: 1995-10-30T00:00:00Z
review text: Two pinching theorems for \(n\)-dimensional submanifolds with parallel mean curvature vector in \(S^{n + p} (1)\) are proved. Both characterize totally umbilical submanifolds and depend on the estimation of \[ \int_ M (S - nH^ 2)^{n/2}, \] where \(S\) is the square of the length of the second fundamental form and \(H\) is the mean curvature.
reviewed by: Barbara Opozda
Mathematics Subject Classification ID: 53C40
Mathematics Subject Classification ID: 53C20
zbMATH DE Number: 757990
zbMATH Keywords: sectional curvatures
zbMATH Keywords: parallel mean curvature vector
zbMATH Keywords: totally umbilical submanifolds
zbMATH Keywords: second fundamental form
author: Hongwei Xu
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2969/jmsj/04630503
OpenAlex ID: W1964899169
DOI: 10.2969/JMSJ/04630503
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description: scientific article; zbMATH DE number 757990