Abstract
Abstract The Einstein-Kahler metric for the Cartan-Hartogs domain of the second type is described. Firstly, the Monge-Amp`ere equation for the metric to an ordinary differential equation in the auxiliary function X = X(z, ω) is reduced, by which an implicit function in X is obtained. Secondly, for some cases, the explicit forms of the complete Einstein-Kahler metrics on Cartan-Hartogs domains which are the non-homogeneous domains are obtained. Thirdly, the estimate of holomorphic sectional curvature under the Einstein-Kahler metric is given, and in some cases the comparison theorem for Kobayashi metric and Einstein-Kahler metric on Cartan-Hartogs domain of the second type is established.
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