底空间为对称域乘积的Hartogs域的度量等价

Metric Equivalence of Hartogs Domains Whose Base Space Is a Product of Symmetric Domain

研究一类非齐性Hartogs域上经典度量的等价问题.首先证明了Bergman-度量和Einstein-Khler度量在这类域上等价;其次,当域的参数满足mσ+nΤ<1时,此类域上Bergman度量,Carathéodary度量,Kobalyashi度量和Einstein-Khler度量是等价的.

We study the equivalent problem of the classical metric on a class of non- homogeneous Hartogs domain. Firstly, it is proved that the equivalence between the Bergman and the Einstein-Kahler metrics on these domains; Secondly, it is shown that the Bergman metric, the Carathaodary metric, the Kobayashi metric and the Einstein- Kahler metric are equivalent, when parameters of the domain satisfy ma ＋ nT 〈 1.