复流形上强拟凸的复Finsler度量  

Stongly pseudoconvex complex Finsler metrics on complex manifold

作　　者：钟春平[1] ZHONG Chunping(School of Mathematical Sciences,Xiamen University,Xiamen 361005,China)

机构地区：[1]厦门大学数学科学学院,福建厦门361005

出　　处：《厦门大学学报（自然科学版）》2023年第6期963-970,共8页Journal of Xiamen University：Natural Science

基　　金：国家自然科学基金(12071386)。

摘　　要：复Finsler几何是研究复流形上度量函数没有Hermite二次型限制的Hermite几何,它包括Hermite二次型与非Hermite二次型度量的几何,尤其侧重后者的研究.本文对一些特殊的强拟凸、非Hermite二次型的复Finsler度量的例子作一简单介绍,内容包括复Berwald度量、弱复Berwald度量、Kahler-Finsler度量以及弱Kahler-Finsler度量之间的关系,它们的具体构造及相关分类.As a study of differential geometry of complex Finsler metrics,which are not necessarily Hermitian quadratic on complex manifolds,the complex Finsler geometry includes Hermitian geometry as a special case,and especially focuses on the study of complex Finsler metrics that are non-Hermitian quadratic.In this paper,we present a simple introduction of some special strongly pseudo convex complex Finsler metrics which are not necessarily Hermitian quadratic,including complex Berwald metrics,weakly complex Berwald metrics,and some relationships between Kahler-Finsler metrics and weakly Kahler-Finsler metrics,its concrete constructions and classifications.We also introduce some explicit constructions of holomorphic invariant strongly convex Kahler-Berwald metrics on the unit polydisk in Cn with n≥2.

关 键 词：复Berwald度量 Kahler-Berwald度量 全纯不变的Kahler-Berwald度量 

分 类 号：O174.56[理学—数学]