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
In this paper,we study the extremal problem on Cartan-egg domain of the first type by using some inequalities.The extremal mapping and extremal value between the first type of Cartan-egg domain and the unit ball when ...In this paper,we study the extremal problem on Cartan-egg domain of the first type by using some inequalities.The extremal mapping and extremal value between the first type of Cartan-egg domain and the unit ball when k≤1 and k=2,m=2 are constructed.展开更多
We discuss Bianchi type-VII0 cosmology with a Dirac field in the Einstein–Cartan(E−C)theory and obtain the equations of the Dirac and gravitational fields in the E-C theory.A Bianchi type-VII0 inflationary solution i...We discuss Bianchi type-VII0 cosmology with a Dirac field in the Einstein–Cartan(E−C)theory and obtain the equations of the Dirac and gravitational fields in the E-C theory.A Bianchi type-VII0 inflationary solution is found.When 3S^(2)/16−σ^(2)>0,the Universe may avoid singularity.展开更多
In this paper,we determine the derivation algebra of non-restricted Lie algebra H(n,m) of Cartan type in characteristic p=2.The main reault is following;Der(Hn,m))=adH(n,m)(H^m(n,m+Fd).
In this paper, the derivation algebra of Lie superalgebra H of Caftan-type over F are determined by the calculating method in the situations of CharF = p ≥ 3 or m ≥ 2 or n ≥ 1. The main result is following： DerFH ...In this paper, the derivation algebra of Lie superalgebra H of Caftan-type over F are determined by the calculating method in the situations of CharF = p ≥ 3 or m ≥ 2 or n ≥ 1. The main result is following： DerFH = adH（H＂ ＋ Fh） （{（adDi）^pt ｜ i = 1,2,…,m, t=1,2,…,ti-1}）.展开更多
We introduce a fundamental connection in Finsler geometry,which is torsion-free and almost compatible with the induced metric. We give the difference between this connection and other known connections.
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.
基金Supported by the SF of Jiangsu Province Education(07KJB110115)
文摘In this paper,we study the extremal problem on Cartan-egg domain of the first type by using some inequalities.The extremal mapping and extremal value between the first type of Cartan-egg domain and the unit ball when k≤1 and k=2,m=2 are constructed.
基金by the National Natural Science Foundation of China under Grant No 10947146,Shanghai Normal University under Grant Nos RE946,DKL934 and PL905the Natural Science Foundation of Jiangsu Province under Grant No 07KJD140011。
文摘We discuss Bianchi type-VII0 cosmology with a Dirac field in the Einstein–Cartan(E−C)theory and obtain the equations of the Dirac and gravitational fields in the E-C theory.A Bianchi type-VII0 inflationary solution is found.When 3S^(2)/16−σ^(2)>0,the Universe may avoid singularity.
文摘In this paper,we determine the derivation algebra of non-restricted Lie algebra H(n,m) of Cartan type in characteristic p=2.The main reault is following;Der(Hn,m))=adH(n,m)(H^m(n,m+Fd).
基金Supported by the Natural Science Foundation of the Henan Institute of Science and Technology（06057）
文摘In this paper, the derivation algebra of Lie superalgebra H of Caftan-type over F are determined by the calculating method in the situations of CharF = p ≥ 3 or m ≥ 2 or n ≥ 1. The main result is following： DerFH = adH（H＂ ＋ Fh） （{（adDi）^pt ｜ i = 1,2,…,m, t=1,2,…,ti-1}）.
文摘We introduce a fundamental connection in Finsler geometry,which is torsion-free and almost compatible with the induced metric. We give the difference between this connection and other known connections.
