• East Asian mathematical journal
• /
• v.16 no.2
• /
• pp.331-337
• /
• 2000

• East Asian mathematical journal
• /
• v.16 no.2
• /
• pp.391-399
• /
• 2000

• East Asian mathematical journal
• /
• v.17 no.1
• /
• pp.159-165
• /
• 2001

• Journal of the Korean Mathematical Society
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• v.40 no.4
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• pp.609-627
• /
• 2003

In this paper we describe the Einstein-Kahler metric for the Cartan-Hartogs of the first type which is the special case of the Hua domains. Firstly, we reduce the Monge-Ampere equation for the metric to an ordinary differential equation in the auxiliary function X = X(z, w) = $\midw\mid^2[det(I-ZZ^{T}]^{\frac{1}{K}}$ (see below). This differential equation can be solved to give an implicit function in Χ. Secondly, we get the estimate of the holomorphic section curvature under the complete Einstein-K$\ddot{a}$hler metric on this domain.