Ricci solitons and odd-dimensional spheres
type: Item
instance of: scholarly article
title: Ricci solitons and odd-dimensional spheres
zbMATH Open document ID: 1219.53037
author: Jong Taek Cho
published in: Monatshefte für Mathematik
publication date: 2010-08-06T00:00:00Z
review text: The reviewed paper is concerned with characterizations of a standard sphere. Let \(M\) be an isometrically immersed oriented real hypersurface in a complex space \(\mathbb C^n\) with a flat Kähler structure \((J,\tilde g)\). The Reeb vector field \(\xi\) is defined by \(\xi=-JN\), where \(N\) is a unit normal vector field on \(M\). The author gives two sufficient conditions (inequalities in terms of the shape operator, the Reeb vector field and its associated 1-form) for a compact real hypersurface \(M\) in \(\mathbb C^n\) to be a standard sphere. Moreover, he proves that, if such an \(M\) admits a Ricci soliton whose potential vector field is the Reeb vector field, then \(M\) is a sphere.
reviewed by: Marian Hotloś
Mathematics Subject Classification ID: 53C20
Mathematics Subject Classification ID: 53C25
Mathematics Subject Classification ID: 53C40
zbMATH DE Number: 5764652
zbMATH Keywords: sphere
zbMATH Keywords: shape operator
zbMATH Keywords: Reeb vector field
zbMATH Keywords: Ricci soliton
MaRDI profile type: Publication
full work available at URL: s00605-009-0095-1
OpenAlex ID: W1989551725
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Wikidata QID: Q125907677
DOI: 10.1007/S00605-009-0095-1
description: scientific article; zbMATH DE number 5764652