Three dimensional contact metric manifolds with Cotton solitons
type: Item
instance of: scholarly article
title: Three dimensional contact metric manifolds with Cotton solitons
zbMATH Open document ID: 1486.53093
author: Xiaomin Chen
published in: Hiroshima Mathematical Journal
publication date: 2022-02-02T00:00:00Z
full work available at URL: h2020064.full
review text: Three-dimensional contact metric manifolds admitting Cotton solitons are considered. Under some special conditions, classifications of three-dimensional contact metric manifolds admitting gradient Cotton solitons and Cotton solitons with potential vector field are obtained. Also under certain conditions, classifications of some types of three-dimensional so-called \((\kappa,\mu,\nu)\)-contact metric manifolds admitting Cotton solitons are presented. In particular, it is proved that if a three-dimensional \((\kappa,\mu,\nu)\)-contact metric manifold admits a Cotton soliton such that the potential vector field \(V\) is the Reeb vector field \(\xi\), then this manifold is Sasakian.
Mathematics Subject Classification ID: 53D10
Mathematics Subject Classification ID: 53C25
Mathematics Subject Classification ID: 53C15
zbMATH DE Number: 7468339
zbMATH Keywords: contact metric \((\kappa,\mu,\nu)\)-manifold
zbMATH Keywords: contact metric manifold
zbMATH Keywords: Cotton soliton
zbMATH Keywords: Sasakian manifold
reviewed by: Mihail B. Banaru
MaRDI profile type: Publication
OpenAlex ID: W3215364175
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DOI: 10.32917/H2020064
description: scientific article; zbMATH DE number 7468339