In this paper we give the proof about the equivalence of the complete Einstein- Kahler metric and the Bergman metric on Cartan-Hartogs domain of the third type. And we obtain the method of getting the equivalence of t...In this paper we give the proof about the equivalence of the complete Einstein- Kahler metric and the Bergman metric on Cartan-Hartogs domain of the third type. And we obtain the method of getting the equivalence of two metrics.展开更多
Abstract In this paper, the author considers a class of bounded pseudoconvex domains, i.e., the generalized Cartan-Hartogs domains Ω（μ, m）. The first result is that the natural Kahler metric gΩ（μ,m） of Ω（μ...Abstract In this paper, the author considers a class of bounded pseudoconvex domains, i.e., the generalized Cartan-Hartogs domains Ω（μ, m）. The first result is that the natural Kahler metric gΩ（μ,m） of Ω（μ, m） is extremal if and only if its scalar curvature is a constant. The second result is that the Bergman metric, the Kahler-Einstein metric, the Caratheodary metric, and the Koboyashi metric are equivalent for Ω（μ, m）.展开更多
In this paper, we discuss the invariant complete metric on the Cartan-Hartogs domain of the fourth type. Firstly, we find a new invariant complete metric, and prove the equivalence between Bergman metric and the new m...In this paper, we discuss the invariant complete metric on the Cartan-Hartogs domain of the fourth type. Firstly, we find a new invariant complete metric, and prove the equivalence between Bergman metric and the new metric; Secondly, the Ricci curvature of the new metric has the super bound and lower bound; Thirdly,we prove that the holomorphic sectional curvature of the new metric has the negative supper bound; Finally, we obtain the equivalence between Bergman metric and Einstein-Kahler metric on the Cartan-Hartogs domain of the fourth type.展开更多
文摘In this paper we give the proof about the equivalence of the complete Einstein- Kahler metric and the Bergman metric on Cartan-Hartogs domain of the third type. And we obtain the method of getting the equivalence of two metrics.
基金supported by the National Natural Science Foundation of China(No.11371257)
文摘Abstract In this paper, the author considers a class of bounded pseudoconvex domains, i.e., the generalized Cartan-Hartogs domains Ω（μ, m）. The first result is that the natural Kahler metric gΩ（μ,m） of Ω（μ, m） is extremal if and only if its scalar curvature is a constant. The second result is that the Bergman metric, the Kahler-Einstein metric, the Caratheodary metric, and the Koboyashi metric are equivalent for Ω（μ, m）.
文摘In this paper, we discuss the invariant complete metric on the Cartan-Hartogs domain of the fourth type. Firstly, we find a new invariant complete metric, and prove the equivalence between Bergman metric and the new metric; Secondly, the Ricci curvature of the new metric has the super bound and lower bound; Thirdly,we prove that the holomorphic sectional curvature of the new metric has the negative supper bound; Finally, we obtain the equivalence between Bergman metric and Einstein-Kahler metric on the Cartan-Hartogs domain of the fourth type.
