Abstract
In this paper we describe the Einstein-Kahler metric for the Cartan-Hartogs domains which are the special case of the Hua domains. First of all, we reduce the Monge-Ampere 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-Kahler metrics on Cartan-Hartogs domains which are the non-homogeneous domains.
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