Geometry of holomorphic invariant strongly pseudoconvex complex Finsler metrics on the classical domains  

作　　者：Xiaoshu Ge Chunping Zhong 

机构地区：[1]School of Mathematical Sciences,Xiamen University,Xiamen 361005,China

出　　处：《Science China Mathematics》2024年第8期1827-1864,共38页中国科学（数学）（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant Nos.12071386 and 11671330)。

摘　　要：In this paper,a class of holomorphic invariant metrics is introduced on the irreducible classical domains of typesⅠ-Ⅳ,which are strongly pseudoconvex complex Finsler metrics in the strict sense of Abate and Patrizio(1994).These metrics are of particular interest in several complex variables since they are holomorphic invariant complex Finsler metrics found in the literature which enjoy good regularity as well as strong pseudoconvexity and can be explicitly expressed to admit differential geometry studies.They are,however,not necessarily Hermitian quadratic as the Bergman metrics.These metrics are explicitly constructed via deformation of the corresponding Bergman metric on the irreducible classical domains of typesⅠ-Ⅳ,respectively,and they are all proved to be complete K?hler-Berwald metrics.They enjoy very similar curvature properties as those of the Bergman metric on the irreducible classical domains,i.e.,their holomorphic sectional curvatures are bounded between two negative constants and their holomorphic bisectional curvatures are always nonpositive and bounded below by negative constants,respectively.From the viewpoint of complex analysis,these metrics are analogs of Bergman metrics in complex Finsler geometry which do not necessarily have Hermitian quadratic restrictions in the sense of Chern(1996).

关 键 词：holomorphic invariant metric Kahler-Berwald metric irreducible classical domains 

分 类 号：O186.1[理学—数学]