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 me...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-Khler metric on the Cartan-Hartogs domain of the fourth type.展开更多
Let YI be the Cartan-Hartogs domain of the first type. We give the generating function of the Einstein-Kahler metrics on YI, the holomorphic sectional curvature of the invariant Einstein-Kahler metrics on YI. The comp...Let YI be the Cartan-Hartogs domain of the first type. We give the generating function of the Einstein-Kahler metrics on YI, the holomorphic sectional curvature of the invariant Einstein-Kahler metrics on YI. The comparison theorem of complete Einstein-Kahler metric and Kobayashi metric on YI is provided for some cases. For the non-homogeneous domain YI, when K = mn+1/m+n, m ＞ 1, the explicit forms of the complete Einstein-Kahler metrics are obtained.展开更多
Let Y_Ⅳ be the Super-Cartan domain of the fourth type. We reduce the Monge-Ampereequation for the metric to an ordinary differential equation in the auxiliary function X=X(Z, W). Thisdifferential equation can be solv...Let Y_Ⅳ be the Super-Cartan domain of the fourth type. We reduce the Monge-Ampereequation for the metric to an ordinary differential equation in the auxiliary function X=X(Z, W). Thisdifferential equation can be solved to give an implicit function in X. We give the generating functionof the Einstein-Kahler metric on Y_Ⅳ. We obtain the explicit form of the complete Einstein-Kahlermetric on Y_Ⅳ for a special case.展开更多
In this paper we give the proof about the equivalence of the complete Einstein- K■hler metric and the Bergman metric on Cartan-Hartogs domain of the third type. And we obtain the method of getting the equivalence of ...In this paper we give the proof about the equivalence of the complete Einstein- K■hler 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
We prove that, under a semi-ampleness type assumption on the twisted canonical line bundle, the conical Khler-Ricci flow on a minimal elliptic Khler surface converges in the sense of currents to a generalized coni...We prove that, under a semi-ampleness type assumption on the twisted canonical line bundle, the conical Khler-Ricci flow on a minimal elliptic Khler surface converges in the sense of currents to a generalized conical Khler-Einstein on its canonical model. Moreover,the convergence takes place smoothly outside the singular fibers and the chosen divisor.展开更多
The first part of this paper we talk about the story of how to introduce the Hua domains and summarize the main results on Hua domains.The second part,the explicit complete Einstein-Khler metric on the special type ...The first part of this paper we talk about the story of how to introduce the Hua domains and summarize the main results on Hua domains.The second part,the explicit complete Einstein-Khler metric on the special type of Hua domains is given and the sharp estimate of holomorphic sectional curvature under this metric is also obtained.In the meantime we also prove that the complete Einstein-Khler metric is equivalent to the Bergman metric on the special type of Hua domain.展开更多
In this paper, we compute the complete Einstein-Kahler metric with explicit formula for the Cartan-Hartogs domain of the fourth type in some cases. Under this metric the holomorphic sectional curvature is given, which...In this paper, we compute the complete Einstein-Kahler metric with explicit formula for the Cartan-Hartogs domain of the fourth type in some cases. Under this metric the holomorphic sectional curvature is given, which intervenes between -2k and -1. This is the sharp estimate.展开更多
In this paper we study the complete invariant metrics on Cartan-Hartogs domains which are the special types of Hua domains. Firstly, we introduce a class of new complete invariant metrics on these domains, and prove t...In this paper we study the complete invariant metrics on Cartan-Hartogs domains which are the special types of Hua domains. Firstly, we introduce a class of new complete invariant metrics on these domains, and prove that these metrics are equivalent to the Bergman metric. Secondly, the Ricci curvatures under these new metrics are bounded from above and below by the negative constants. Thirdly, we estimate the holomorphic sectional curvatures of the new metrics, and prove that the holomorphic sectional curvatures are bounded from above and below by the negative constants. Finally, by using these new metrics and Yau’s Schwarz lemma we prove that the new metrics are equivalent to the Einstein-Kahler metric. That means that the Yau’s conjecture is true on Cartan-Hartogs domains.展开更多
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-Khler metric on the Cartan-Hartogs domain of the fourth type.
基金This work was supported by the National Natural Science Foundation of China(Grant Nos.10071051 and 10171068)Natural Science Foundation of Beijing(Grant Nos.1002004 and 1012004).
文摘Let YI be the Cartan-Hartogs domain of the first type. We give the generating function of the Einstein-Kahler metrics on YI, the holomorphic sectional curvature of the invariant Einstein-Kahler metrics on YI. The comparison theorem of complete Einstein-Kahler metric and Kobayashi metric on YI is provided for some cases. For the non-homogeneous domain YI, when K = mn+1/m+n, m ＞ 1, the explicit forms of the complete Einstein-Kahler metrics are obtained.
基金Supported by National Natural Science Foundation of China(Grant No.10471097)Scientific Research Common Program of Beijing Municipal Commission of Education(Grant NO.KM200410028002)Supported by National Natural Science Foundation of China(Grant No
文摘Let Y_Ⅳ be the Super-Cartan domain of the fourth type. We reduce the Monge-Ampereequation for the metric to an ordinary differential equation in the auxiliary function X=X(Z, W). Thisdifferential equation can be solved to give an implicit function in X. We give the generating functionof the Einstein-Kahler metric on Y_Ⅳ. We obtain the explicit form of the complete Einstein-Kahlermetric on Y_Ⅳ for a special case.
文摘In this paper we give the proof about the equivalence of the complete Einstein- K■hler 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 Science and Technology Development Fund(Macao S.A.R.),Grant FDCT/016/2013/A1the Project MYRG2015-00235-FST of the University of Macao
文摘We prove that, under a semi-ampleness type assumption on the twisted canonical line bundle, the conical Khler-Ricci flow on a minimal elliptic Khler surface converges in the sense of currents to a generalized conical Khler-Einstein on its canonical model. Moreover,the convergence takes place smoothly outside the singular fibers and the chosen divisor.
基金Projectsupported in part by NSF of China(Grant NO.10471097 and the Doctoral Programme Foundation of NEM of China
文摘The first part of this paper we talk about the story of how to introduce the Hua domains and summarize the main results on Hua domains.The second part,the explicit complete Einstein-Khler metric on the special type of Hua domains is given and the sharp estimate of holomorphic sectional curvature under this metric is also obtained.In the meantime we also prove that the complete Einstein-Khler metric is equivalent to the Bergman metric on the special type of Hua domain.
文摘In this paper, we compute the complete Einstein-Kahler metric with explicit formula for the Cartan-Hartogs domain of the fourth type in some cases. Under this metric the holomorphic sectional curvature is given, which intervenes between -2k and -1. This is the sharp estimate.
基金partially supported by the National Natural Science Foundation of China(Grant No.10471097)the Scientific Research Common Program of Beijing Municipal Commission of Education(Grant No.KM200410028002)the Doctoral Programme Foundation of Ministry of Education of China(Grant No.20040028003)
文摘In this paper we study the complete invariant metrics on Cartan-Hartogs domains which are the special types of Hua domains. Firstly, we introduce a class of new complete invariant metrics on these domains, and prove that these metrics are equivalent to the Bergman metric. Secondly, the Ricci curvatures under these new metrics are bounded from above and below by the negative constants. Thirdly, we estimate the holomorphic sectional curvatures of the new metrics, and prove that the holomorphic sectional curvatures are bounded from above and below by the negative constants. Finally, by using these new metrics and Yau’s Schwarz lemma we prove that the new metrics are equivalent to the Einstein-Kahler metric. That means that the Yau’s conjecture is true on Cartan-Hartogs domains.
