The author determines the real-analytic infinitesimal CR automorphisms of a class of non-homogeneous rigid hypersurfaces in CN+1 near the origin,and the connected component containing the identity transformation of al...The author determines the real-analytic infinitesimal CR automorphisms of a class of non-homogeneous rigid hypersurfaces in CN+1 near the origin,and the connected component containing the identity transformation of all locally holomorphic auto-morphisms of these hypersurfaces near the origin.展开更多
In this paper, we compute the Bergman kernel function on WIII.and RIII(q) denote the Cartan domain of the third class. Because domain WIII is neither homogeneous domain nor Reinhardt domain, we will use a new way to s...In this paper, we compute the Bergman kernel function on WIII.and RIII(q) denote the Cartan domain of the third class. Because domain WIII is neither homogeneous domain nor Reinhardt domain, we will use a new way to solve this problem. First, we give a holomorphic automorphism group, such that for any Zo, there exists an element of this group, which maps (W, Zo) into (W,O). Second, introduce the concept of semi-Reinhardt and discuss the complete orthonormal system of this domain.展开更多
We known that the maximal connected holomorphic automorphism group Aut(D)(0)is a semi-direct product of the triangle group T(D)and the maximal connected isotropic subgroup Iso(D)(0)of a fixed point in the complex homo...We known that the maximal connected holomorphic automorphism group Aut(D)(0)is a semi-direct product of the triangle group T(D)and the maximal connected isotropic subgroup Iso(D)(0)of a fixed point in the complex homogeneous bounded domain D and any complex homogeneous bounded domain is holomorphic isomorphic to a normal Siegel domain D(VN,F).In this paper,we give the explicit formula of any holomorphic automorphism in T(D(VN,F))and Iso(D(VN,F))(0),where G(0)is the unit connected component of the Lie group G.展开更多
In this paper, we give an explicit formula of the Bergman kernel function on Hua Construction of the second type when the parameters 1/p1,…, 1/pr-1 are positive integers and 1/pr is an arbitrary positive real number.
In this paper we discuss the Einstein-Kahler metric on the third Cartan-Hartogs domain Y111（n, q; K）. Firstly we get the complete Einstein Kahler metric with explicit form on Y111（n, q; K） in the case of K=q/2 ＋ ...In this paper we discuss the Einstein-Kahler metric on the third Cartan-Hartogs domain Y111（n, q; K）. Firstly we get the complete Einstein Kahler metric with explicit form on Y111（n, q; K） in the case of K=q/2 ＋ 1/q-1. Secondly we obtain the holomorphic sectional curvature under this metric and get the sharp estimate for this holomorphic curvature. Finally we prove that the complete Einstein-Kahler metric is equivalent to the Bergman metric on Y111（n, q; K） in case of K=q/2＋1/q-1.展开更多
基金supported by the National Natural Science Foundation of China(No.10871172)
文摘The author determines the real-analytic infinitesimal CR automorphisms of a class of non-homogeneous rigid hypersurfaces in CN+1 near the origin,and the connected component containing the identity transformation of all locally holomorphic auto-morphisms of these hypersurfaces near the origin.
文摘In this paper, we compute the Bergman kernel function on WIII.and RIII(q) denote the Cartan domain of the third class. Because domain WIII is neither homogeneous domain nor Reinhardt domain, we will use a new way to solve this problem. First, we give a holomorphic automorphism group, such that for any Zo, there exists an element of this group, which maps (W, Zo) into (W,O). Second, introduce the concept of semi-Reinhardt and discuss the complete orthonormal system of this domain.
基金This work was supported by the National Natural Science Foundation of China(Grant No.10171027).
文摘We known that the maximal connected holomorphic automorphism group Aut(D)(0)is a semi-direct product of the triangle group T(D)and the maximal connected isotropic subgroup Iso(D)(0)of a fixed point in the complex homogeneous bounded domain D and any complex homogeneous bounded domain is holomorphic isomorphic to a normal Siegel domain D(VN,F).In this paper,we give the explicit formula of any holomorphic automorphism in T(D(VN,F))and Iso(D(VN,F))(0),where G(0)is the unit connected component of the Lie group G.
文摘In this paper, we give an explicit formula of the Bergman kernel function on Hua Construction of the second type when the parameters 1/p1,…, 1/pr-1 are positive integers and 1/pr is an arbitrary positive real number.
文摘In this paper we discuss the Einstein-Kahler metric on the third Cartan-Hartogs domain Y111（n, q; K）. Firstly we get the complete Einstein Kahler metric with explicit form on Y111（n, q; K） in the case of K=q/2 ＋ 1/q-1. Secondly we obtain the holomorphic sectional curvature under this metric and get the sharp estimate for this holomorphic curvature. Finally we prove that the complete Einstein-Kahler metric is equivalent to the Bergman metric on Y111（n, q; K） in case of K=q/2＋1/q-1.
