{"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":49887,"journal":{"name":"Manuscripta Mathematica","volume":"52 1","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2024-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Manuscripta Mathematica","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00229-024-01542-6","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
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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 \(n\ge 3\).
期刊介绍：
manuscripta mathematica was founded in 1969 to provide a forum for the rapid communication of advances in mathematical research. Edited by an international board whose members represent a wide spectrum of research interests, manuscripta mathematica is now recognized as a leading source of information on the latest mathematical results.
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