{"title":"Rigidity of bach-flat gradient schouten solitons","authors":"Valter Borges","doi":"10.1007/s00229-024-01542-6","DOIUrl":null,"url":null,"abstract":"<p>In this paper, we show that complete Bach-flat Schouten solitons with <span>\\(n\\ge 4\\)</span> are rigid. When <span>\\(n=3\\)</span> we are able to conclude rigidity under a more general condition, namely when the Bach tensor is divergence-free. These results imply rigidity of locally conformally flat Schouten solitons for <span>\\(n\\ge 3\\)</span>.</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00229-024-01542-6","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we show that complete Bach-flat Schouten solitons with \(n\ge 4\) are rigid. When \(n=3\) we are able to conclude rigidity under a more general condition, namely when the Bach tensor is divergence-free. These results imply rigidity of locally conformally flat Schouten solitons for \(n\ge 3\).