论文标题
全体形态不变的几何形状在经典域上强烈伪造复杂的鳍片指标
Geometry of holomorphic invariant strongly pseudoconvex complex Finsler metrics on the classical domains
论文作者
论文摘要
在本文中，I-IV的不可还原经典领域引入了一类全体形态不变的指标，它们在严格的M. Abate和G. Patrizio [2]中是强烈的Pseudoconvex复杂的Finsler指标[2]。这些指标在几个复杂的变量中特别感兴趣，因为它们是迄今为止在文献中发现的整体形态不变的复杂的鳍指标，它们具有良好的规律性和强大的假性通用性，并且可以明确表达，以便接受差异几何研究。但是，它们不一定是伯格曼指标的二次二次二次。这些指标分别是通过对I-IV型不可约的经典域上的相应伯格曼度量的变形来明确构建的，事实证明它们都是完整的Kahler-Berwald指标。它们具有非常相似的曲率特性，与伯格曼度量标准的曲率特性相似，即它们的圆形截面曲率在两个负常数之间有界限，并且它们的全态双形曲率始终是非正面的，并且分别由负恒定限制在下面。从复杂分析的角度来看，这些指标是复杂的芬斯勒几何形状中伯格曼指标的类似物，在S.-S的观点中，不一定具有Hermitian二次限制。 Chern [7]。
In this paper, a class of holomorphic invariant metrics is introduced on the irreducible classical domains of type I-IV, which are strongly pseudoconvex complex Finsler metrics in the strict sense of M. Abate and G. Patrizio[2]. These metrics are of particular interest in several complex variables since they are holomorphic invariant complex Finsler metrics found so far in literature which enjoy good regularity as well as strong pseudoconvexity and can be explicitly expressed so as to admit differential geometric studies. They are, however, not necessarily Hermitian quadratic as that of the Bergman metrics. These metrics are explicitly constructed via deformation of the corresponding Bergman metric on the irreducible classical domains of type I-IV, respectively, and they are all proved to be complete Kahler-Berwald metrics. They enjoy very similar curvature properties as that of the Bergman metric on the irreducible classical domains, namely their holomorphic sectional curvatures are bounded between two negative constants, and their holomorphic bisectional curvatures are always non positive and bounded below by negative constants, respectively. From the viewpoint of complex analysis, these metrics are analogues of Bergman metrics in complex Finsler geometry which do not necessarily have Hermitian quadratic restrictions in the viewpoint of S.-S. Chern[7].
