{"title":"On the \\(\\Delta \\)-property for complex space forms","authors":"Roberto Mossa","doi":"10.1007/s12188-021-00233-3","DOIUrl":null,"url":null,"abstract":"<div><p>Inspired by the work of Lu and Tian (Duke Math J 125:351--387, 2004), Loi et al. address in (Abh Math Semin Univ Hambg 90: 99-109, 2020) the problem of studying those Kähler manifolds satisfying the <span>\\(\\Delta \\)</span>-property, i.e. such that on a neighborhood of each of its points the <i>k</i>-th power of the Kähler Laplacian is a polynomial function of the complex Euclidean Laplacian, for all positive integer <i>k</i>. In particular they conjectured that if a Kähler manifold satisfies the <span>\\(\\Delta \\)</span>-property then it is a complex space form. This paper is dedicated to the proof of the validity of this conjecture.</p></div>","PeriodicalId":50932,"journal":{"name":"Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg","volume":null,"pages":null},"PeriodicalIF":0.4000,"publicationDate":"2021-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s12188-021-00233-3","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s12188-021-00233-3","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
Inspired by the work of Lu and Tian (Duke Math J 125:351--387, 2004), Loi et al. address in (Abh Math Semin Univ Hambg 90: 99-109, 2020) the problem of studying those Kähler manifolds satisfying the \(\Delta \)-property, i.e. such that on a neighborhood of each of its points the k-th power of the Kähler Laplacian is a polynomial function of the complex Euclidean Laplacian, for all positive integer k. In particular they conjectured that if a Kähler manifold satisfies the \(\Delta \)-property then it is a complex space form. This paper is dedicated to the proof of the validity of this conjecture.
受Lu和Tian（Duke Math J 125:351-3872004）工作的启发，Loi等人在（Abh Math Semin Univ Hambg 90:99-1092020）中提出了研究那些满足\（\Delta\）性质的Kähler流形的问题，即在其每个点的邻域上，特别是他们猜想，如果kähler流形满足\（\Delta）-性质，则它是一个复空间形式。本文致力于证明这一猜想的有效性。
期刊介绍：
The first issue of the "Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg" was published in the year 1921. This international mathematical journal has since then provided a forum for significant research contributions. The journal covers all central areas of pure mathematics, such as algebra, complex analysis and geometry, differential geometry and global analysis, graph theory and discrete mathematics, Lie theory, number theory, and algebraic topology.
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