Abstract
Let YI be the Cartan-Hartogs domain of the first type. We give the generating function of the Einstein-Kahler metrics on YI, the holomorphic sectional curvature of the invariant Einstein-Kahler metrics on YI . The comparison theorem of complete Einstein-Kahler metric and Kobayashi metric on YI is provided for some cases. For the non-homogeneous domain YI, when \(K = \frac{{mn + 1}}{{m + n}},m > 1\), the explicit forms of the complete Einstein-Kahler metrics are obtained.
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