Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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THE EINSTEIN-KÄHLER METRICS ON HUA DOMAIN

  • Wang, An (Department of Mathematics Capital Normal University) ;
  • Yin, Weiping (Department of Mathematics Capital Normal University)
  • Published : 2003.07.01
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Abstract

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.

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References

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Cited by

  1. On the solution of Dirichlet problem of complex Monge-Ampère equation on Cartan-Hartogs domain of the second type vol.52, pp.12, 2009, https://doi.org/10.1007/s11425-009-0221-5