\(L_{n/2}\)-pinching theorem for submanifolds in a sphere
type: Item
instance of: scholarly article
title: \(L_{n/2}\)-pinching theorem for submanifolds in a sphere
zbMATH Open document ID: 1141.53050
author: Hui-Qun Xu
published in: Kodai Mathematical Journal
publication date: 2008-03-06T00:00:00Z
review text: The author proves that for any \(n\geq 2\) there exists a constant \(C(n) >0\) such that any oriented closed \(n\)-dimensional submanifold \(M\) of the unit sphere is totally umbilical if only if the mean curvature vector of \(M\) is parallel and the second fundamental form \(A\) of \(M\) satisfies the inequality \(\int _M\| A\| ^n < C(n)\).
Mathematics Subject Classification ID: 53C40
zbMATH DE Number: 5244037
zbMATH Keywords: sphere
zbMATH Keywords: submanifold
zbMATH Keywords: mean curvature
zbMATH Keywords: umbilicity
reviewed by: Paweł Walczak
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2996/kmj/1183475515
OpenAlex ID: W1981122582
DOI: 10.2996/KMJ/1183475515
description: scientific article