单位圆盘上Bergman圆的性质

The Properties of Bergman Metric Disk on Unit Disk

运用单位圆盘上Pseudo-hyperbolic度量的性质,得到Bergman圆的欧式结构,欧式圆盘与Bergman圆的关系以及Bergman圆上全纯映射的性质。这些性质表明了全纯映射、对合自同构以及Bergman圆之间的密切联系,其在多复变函数理论和函数空间的研究中有理论意义。

This article aims to study the properties of Bergman metric disk on unit disk.In the paper,we give the structure of Bergman metric disk in Euclidean space,the relation between Bergman metric disk and Euclidean disk,and the property of analytic mapping in Bergman metric disk by using the properties of Pseudo-hyperbolic metric on unit disk.All the properties gained in this thesis show the close relation among analytic mapping,involutorial automorphism and Bergman metric disk.They have theoretical significance in the study of the multicomplex function theory and the spaces of function.