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The Einstein-K\＂ahler metrics onHua domain
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Abstract
In this paper we describe the Einstein-K"ahler metric for theCartan-Hartogs of the first type which is the special case of theHua domains. Firstly, we reduce the Monge-Amp` ere equation forthe metric to an ordinary differential equation in the auxiliaryfunction X=X(z,w)=|w|^2[det(I-ZZ^T)]^{-frac{1}{K}}(see below).This differentialequation can be solved to give an implicit function in X.Secondly, we get the estimate of the holomorphic section curvatureunder the complete Einstein-K"ahler metric on this domain.
관련 논문AI추천
A certain K\"ahler potential of the Poincar\'e metric and its characterization이강혁, 최영준, Sungmin Yoo대한수학회 · 대한수학회지2020 · 제57권 제6호Almost K\＂ahler metrics with non-positive scalar curvature which are Euclidean away from a compact setJongsu Kim, Yutae Kang대한수학회 · 대한수학회지2004 · 제41권 제5호Almost K\＂ahler deformation of scalar curvature김종수대한수학회 · 대한수학회논문집2006 · 제21권 제1호THE EXTREMAL PROBLEM ON HUA DOMAINSujuan Long대한수학회 · 대한수학회지2017 · 제54권 제6호HIGHER ORDER ASYMPTOTIC BEHAVIOR OF CERTAIN K¨ AHLER METRICS AND UNIFORMIZATION FOR STRONGLY PSEUDOCONVEX DOMAINS서애령, 주재천대한수학회 · 대한수학회지2015 · 제52권 제1호Notes on K\＂{a}hler surfaces with distinct constant Ricci eigenvaluesKouei Sekigawa, Takashi Oguro, Terumasa Nihonyanagi대한수학회 · 대한수학회지2003 · 제40권 제6호
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