{"title":"巴赫平梯度舒顿孤子的刚性","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":"{\"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}","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}
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 \(n\ge 3\).
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