{"title":"Commutator Formulas for Gradient Ricci Shrinkers and Their Application to Linear Stability of Gradient Ricci Shrinkers","authors":"Mansour Mehrmohamadi, Asadollah Razavi","doi":"10.1007/s41980-024-00890-z","DOIUrl":null,"url":null,"abstract":"<p>In this paper we have found a number of commutator formulas between the weighted divergence, the weighted Laplacian, the weighted Lichnerowicz Laplacian and the Lie derivtive on closed orientable gradient Ricci shrinkers, then using them we have generalized a Theorem of Cao and Zhu about the necessary condition for linear stability of a gradient Ricci shrinker. Recentlly they have also extended our results.</p>","PeriodicalId":9395,"journal":{"name":"Bulletin of The Iranian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2024-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Bulletin of The Iranian Mathematical Society","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s41980-024-00890-z","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper we have found a number of commutator formulas between the weighted divergence, the weighted Laplacian, the weighted Lichnerowicz Laplacian and the Lie derivtive on closed orientable gradient Ricci shrinkers, then using them we have generalized a Theorem of Cao and Zhu about the necessary condition for linear stability of a gradient Ricci shrinker. Recentlly they have also extended our results.
期刊介绍：
The Bulletin of the Iranian Mathematical Society (BIMS) publishes original research papers as well as survey articles on a variety of hot topics from distinguished mathematicians. Research papers presented comprise of innovative contributions while expository survey articles feature important results that appeal to a broad audience. Articles are expected to address active research topics and are required to cite existing (including recent) relevant literature appropriately. Papers are critically reviewed on the basis of quality in its exposition, brevity, potential applications, motivation, value and originality of the results. The BIMS takes a high standard policy against any type plagiarism. The editorial board is devoted to solicit expert referees for a fast and unbiased review process.
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