{"title":"A note on closed quasi-Einstein manifolds","authors":"Wagner Oliveira Costa-Filho","doi":"10.1007/s13324-024-00967-2","DOIUrl":null,"url":null,"abstract":"<p>The notion of <i>m</i>-quasi-Einstein manifolds originates from the study of Einstein warped product metrics and they are influential in constructing for many physical models. For example, these manifolds arises for extremal isolated horizons in the theory of black holes. In a recent work by Cochran (arXiv:2404.17090v1, 2024), the author studied Killing vector fields on closed <i>m</i>-quasi-Einstein manifolds. In this short paper, we will give another proof of his main result involving the scalar curvature, which holds for all values of <i>m</i> and is based on the use of known formulae related to quasi-Einstein metrics.\n</p>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.4000,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Analysis and Mathematical Physics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s13324-024-00967-2","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
The notion of m-quasi-Einstein manifolds originates from the study of Einstein warped product metrics and they are influential in constructing for many physical models. For example, these manifolds arises for extremal isolated horizons in the theory of black holes. In a recent work by Cochran (arXiv:2404.17090v1, 2024), the author studied Killing vector fields on closed m-quasi-Einstein manifolds. In this short paper, we will give another proof of his main result involving the scalar curvature, which holds for all values of m and is based on the use of known formulae related to quasi-Einstein metrics.
m-quasi-Einstein 流形的概念源于对爱因斯坦扭曲积度量的研究，它们对构建许多物理模型都有影响。例如，在黑洞理论中，这些流形用于极端孤立地平线。在科克兰的最新著作（arXiv:2404.17090v1, 2024）中，作者研究了封闭米准爱因斯坦流形上的基林向量场。在这篇短文中，我们将对他涉及标量曲率的主要结果给出另一个证明，该结果对所有 m 值都成立，并且是基于使用与准爱因斯坦流形有关的已知公式。
期刊介绍：
Analysis and Mathematical Physics (AMP) publishes current research results as well as selected high-quality survey articles in real, complex, harmonic; and geometric analysis originating and or having applications in mathematical physics. The journal promotes dialog among specialists in these areas.
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