THE EINSTEIN KÄHLER METRIC WITH EXPLICIT FORMULAS ON SOME NON-HOMOGENEOUS DOMAINS

Abstract

In this paper we describe the Einstein-Kähler metric for the Cartan-Hartogs domains which are the special case of the Hua domains. First of all, we reduce the Monge-Ampére equation for the metric to an ordinary differential equation in the auxiliary function X = X(z,w). This differential equation can be solved to give an implicit function in X. Secondly, for some cases, we obtained explicit forms of the complete Einstein-Kähler metrics on Cartan-Hartogs domains which are the non-homogeneous domains.