{"title":"非爱因斯坦的相对Yamabe度量","authors":"Shota Hamanaka","doi":"10.2996/kmj44202","DOIUrl":null,"url":null,"abstract":"In this paper, we give a sufficient condition for a positive constant scalar curvature metric on a manifold with boundary to be a relative Yamabe metric, which is a natural relative version of the classical Yamabe metric. We also give examples of non-Einstein relative Yamabe metrics with positive scalar curvature.","PeriodicalId":8430,"journal":{"name":"arXiv: Differential Geometry","volume":"187 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2020-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Non-Einstein relative Yamabe metrics\",\"authors\":\"Shota Hamanaka\",\"doi\":\"10.2996/kmj44202\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we give a sufficient condition for a positive constant scalar curvature metric on a manifold with boundary to be a relative Yamabe metric, which is a natural relative version of the classical Yamabe metric. We also give examples of non-Einstein relative Yamabe metrics with positive scalar curvature.\",\"PeriodicalId\":8430,\"journal\":{\"name\":\"arXiv: Differential Geometry\",\"volume\":\"187 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-10-12\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv: Differential Geometry\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.2996/kmj44202\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv: Differential Geometry","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2996/kmj44202","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
In this paper, we give a sufficient condition for a positive constant scalar curvature metric on a manifold with boundary to be a relative Yamabe metric, which is a natural relative version of the classical Yamabe metric. We also give examples of non-Einstein relative Yamabe metrics with positive scalar curvature.
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