• Journal of the Korean Mathematical Society
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• v.57 no.6
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• pp.1335-1345
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• 2020

We will show a rigidity of a Kähler potential of the Poincaré metric with a constant length differential.

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

• Journal of the Korean Mathematical Society
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• v.41 no.5
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• pp.809-820
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• 2004

On $R^{2n}$, n$\geq$2, with the standard symplectic structure we construct compatible almost K hler metrics with negative scalar curvature on a polydisc which are Euclidean away from the polydisc.c.

• Journal of the Korean Mathematical Society
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• v.52 no.1
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• pp.113-124
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• 2015

We provide some relations between CR invariants of boundaries of strongly pseudoconvex domains and higher order asymptotic behavior of certain complete K$\ddot{a}$hler metrics of given domains. As a consequence, we prove a rigidity theorem of strongly pseudoconvex domains by asymptotic curvature behavior of metrics.