{"title":"When are shrinking gradient Ricci soliton compact","authors":"Yuanyuan Qu, Guoqiang Wu","doi":"10.1016/j.difgeo.2023.102102","DOIUrl":null,"url":null,"abstract":"<div><p>Suppose <span><math><mo>(</mo><msup><mrow><mi>M</mi></mrow><mrow><mn>4</mn></mrow></msup><mo>,</mo><mi>g</mi><mo>,</mo><mi>f</mi><mo>)</mo></math></span> is a complete shrinking gradient Ricci soliton. We give a sufficient condition for a soliton to be compact, generalizing previous result of Munteanu-Wang <span>[17]</span>. As an application, we give a classification of <span><math><mo>(</mo><msup><mrow><mi>M</mi></mrow><mrow><mn>4</mn></mrow></msup><mo>,</mo><mi>g</mi><mo>,</mo><mi>f</mi><mo>)</mo></math></span> under some natural conditions.</p></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2024-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Differential Geometry and its Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0926224523001286","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
Suppose is a complete shrinking gradient Ricci soliton. We give a sufficient condition for a soliton to be compact, generalizing previous result of Munteanu-Wang [17]. As an application, we give a classification of under some natural conditions.
期刊介绍：
Differential Geometry and its Applications publishes original research papers and survey papers in differential geometry and in all interdisciplinary areas in mathematics which use differential geometric methods and investigate geometrical structures. The following main areas are covered: differential equations on manifolds, global analysis, Lie groups, local and global differential geometry, the calculus of variations on manifolds, topology of manifolds, and mathematical physics.
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