{"title":"Conformal vector fields on lcK manifolds","authors":"Andrei Moroianu, Mihaela Pilca","doi":"10.4310/mrl.2023.v30.n5.a12","DOIUrl":null,"url":null,"abstract":"We show that any conformal vector field on a compact lcK manifold is Killing with respect to the Gauduchon metric. Furthermore, we prove that any conformal vector field on a compact lcK manifold whose Kähler cover is neither flat, nor hyperkähler, is holomorphic.","PeriodicalId":49857,"journal":{"name":"Mathematical Research Letters","volume":"25 1","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2024-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Research Letters","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4310/mrl.2023.v30.n5.a12","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
We show that any conformal vector field on a compact lcK manifold is Killing with respect to the Gauduchon metric. Furthermore, we prove that any conformal vector field on a compact lcK manifold whose Kähler cover is neither flat, nor hyperkähler, is holomorphic.
期刊介绍:
Dedicated to publication of complete and important papers of original research in all areas of mathematics. Expository papers and research announcements of exceptional interest are also occasionally published. High standards are applied in evaluating submissions; the entire editorial board must approve the acceptance of any paper.