Canonical Metrics On General Hartogs Triangle Domains

In this paper,we apply the cohomogeneity one method to give K?hler-Einstein metric for the general Hartogs triangle domains which are the special case of the generalized Bergman-Hua circular domains.The full text is divided into two chapters.In the first chapter,we introduces the research background of this thesis,the preliminary knowledge and the main research results of this paper.In the second chapter,First of all,We study the Holomorphic automorphism group of some special and give its group structure and its related properties;With these observations,We construct the Auxiliary function X=(z,w)= |w|,we transform the Monge-Ampère equation into an ordinary differential equation,which can be solved as an explicit function of and .Then we give the K?hler-Einstein metric of cohomogeneity one on these special .We notice that our formula of K?hler-Einstein metrics still work for any general .Although there have been many results about canonical metrics on complex manifolds,for different manifolds,the expression of the canonical metrics are often different.Therefore it is meaningful to study canonical metrics in general Hartogs triangle domains.In this paper,some new results are obtained,and the theoretical study of canonical metric on generalized Bergman-Hua circular domains is further pursued.