Asian Journal of Mathematics

Volume 8 (2004)

Number 1

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

Pages: 39 – 50

DOI: http://dx.doi.org/10.4310/AJM.2004.v8.n1.a5

Authors

AN WANG

WEIPING YIN

LIYOU ZHANG

WENJUAN ZHANG

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.

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