{"title":"常数负标量-魏尔曲率的度量","authors":"Giovanni Catino","doi":"10.4310/mrl.2023.v30.n2.a2","DOIUrl":null,"url":null,"abstract":"Extending Aubin's construction of metrics with constant negative scalar curvature, we prove that every $n$-dimensional closed manifold admits a Riemannian metric with constant negative scalar-Weyl curvature, that is $R+t|W|, t\\in\\mathbb{R}$. In particular, there are no topological obstructions for metrics with $\\varepsilon$-pinched Weyl curvature and negative scalar curvature.","PeriodicalId":49857,"journal":{"name":"Mathematical Research Letters","volume":"70 1","pages":"0"},"PeriodicalIF":0.6000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Metrics of constant negative scalar-Weyl curvature\",\"authors\":\"Giovanni Catino\",\"doi\":\"10.4310/mrl.2023.v30.n2.a2\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Extending Aubin's construction of metrics with constant negative scalar curvature, we prove that every $n$-dimensional closed manifold admits a Riemannian metric with constant negative scalar-Weyl curvature, that is $R+t|W|, t\\\\in\\\\mathbb{R}$. In particular, there are no topological obstructions for metrics with $\\\\varepsilon$-pinched Weyl curvature and negative scalar curvature.\",\"PeriodicalId\":49857,\"journal\":{\"name\":\"Mathematical Research Letters\",\"volume\":\"70 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2023-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematical Research Letters\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.4310/mrl.2023.v30.n2.a2\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Research Letters","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4310/mrl.2023.v30.n2.a2","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
Metrics of constant negative scalar-Weyl curvature
Extending Aubin's construction of metrics with constant negative scalar curvature, we prove that every $n$-dimensional closed manifold admits a Riemannian metric with constant negative scalar-Weyl curvature, that is $R+t|W|, t\in\mathbb{R}$. In particular, there are no topological obstructions for metrics with $\varepsilon$-pinched Weyl curvature and negative scalar curvature.
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