The Second Class Of Super-cartan Domain Of The Complete Einstein-k (?) Hler Metric On Its Holomorphic Sectional Curvature

We consider the Cartan-Hartogs domain of the second type :YII(2, p; K) = where RII(p) is the second type of Cartan domain in the sense of L.G.Hua, " det " denotes the " determinant ", " p " belongs to Nature Numbers .We get two main results:1.We present the explicit form of the complete Einstein-Kahler metric on Cartan-Hartogs domain 2. We get the expressions of holomorphic sectional curvature under above Einstein-Kahler metric and prove this curvature has upper bound and lower bound .Due to the result of Mok and Yau ,we know that any bounded pseudoconvex domain Ω in Cn has a unique complete Einstein-Kahler metric . Let the Einstein-Kahler metric on Ω bethen g is the unique solution of the following Dirichlet problem of Monge-Ampere equation :where g is called generating function of the Einstein-Kahler metric on Ω.If the explicit form of generating function g is given ,then the explicit form of the complete Einstein-Kahler metric on Cartan-Hartogs domain YII(2,p;K) is also given.Therefore,we must prove that the Cartan-Hartogs domains YII(2,p; K) is bounded pseudoconvex domain in advance.Then,we will prove that the generating function g of the complete Einstein-Kahler metrics on Cartan-Hartogs domains YII(2,p;K) isThe method is to prove that g is a solution of the Dirichlet problem (1).Finally ,by using some skills and calculation,we present the form of holomorphic sectional curvature w under the Einstein-Kahler metric and prove that...