{"title":"Holomorphic Sectional Curvature of Complex Finsler Manifolds.","authors":"Xueyuan Wan","doi":"10.1007/s12220-018-9985-6","DOIUrl":null,"url":null,"abstract":"<p><p>In this paper, we get an inequality in terms of holomorphic sectional curvature of complex Finsler metrics. As applications, we prove a Schwarz Lemma from a complete Riemannian manifold to a complex Finsler manifold. We also show that a strongly pseudoconvex complex Finsler manifold with semi-positive but not identically zero holomorphic sectional curvature has negative Kodaira dimension under an extra condition.</p>","PeriodicalId":56121,"journal":{"name":"Journal of Geometric Analysis","volume":"29 1","pages":"194-216"},"PeriodicalIF":1.2000,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s12220-018-9985-6","citationCount":"11","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Geometric Analysis","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s12220-018-9985-6","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2018/1/25 0:00:00","PubModel":"Epub","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 11
Abstract
In this paper, we get an inequality in terms of holomorphic sectional curvature of complex Finsler metrics. As applications, we prove a Schwarz Lemma from a complete Riemannian manifold to a complex Finsler manifold. We also show that a strongly pseudoconvex complex Finsler manifold with semi-positive but not identically zero holomorphic sectional curvature has negative Kodaira dimension under an extra condition.
期刊介绍:
JGA publishes both research and high-level expository papers in geometric analysis and its applications. There are no restrictions on page length.