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
Let k be an algebraically closed field of characteristic p 〉 2, and gl（m｜n） be the general linear Lie superalgebra over k. The Cartan invariants for the restricted supermodule category for gl（m｜n） are presented.
A generalized first Noether theorem (GFNT) originating from the invariance under the finite continuous group for singular high-order Lagrangian and a generalized second Noether theorem (or generalized Noether identiti...A generalized first Noether theorem (GFNT) originating from the invariance under the finite continuous group for singular high-order Lagrangian and a generalized second Noether theorem (or generalized Noether identities (GNI)) for variant system under the infinite continuous group of field theory in canonical formalism are derived. The strong and weak conservation laws in canonical formalism are also obtained. It is pointed out that some variant systems also have Dirac constraint. Based on the canonical action, the generalized Poincaré-Cartan integral invariant (GPCⅡ) for singular high-order Lagrangian in the field theory is deduced. Some confusions in literafure are clarified. The GPCⅡ connected with canonical equations and canonical transformation are discussed.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-Kahler metric on the Cartan-Hartogs domain of the fourth type.
基金Supported by the Natural Science Foundation of Henan Province(No.092300410199)Science Foundation for the Excellent Youth Scholars of Henan Province(No.[2005]461)
基金Supported partially by National Natural Science Foundation of China(Grant Nos.11271130,11201293,111126062)The Innovation Program of Shanghai Municipal Education Commission(Grant No.12zz038)Shanghai Science Foundation for Excellent Young Scholars(Grant No.yyy10046)
文摘Let k be an algebraically closed field of characteristic p 〉 2, and gl（m｜n） be the general linear Lie superalgebra over k. The Cartan invariants for the restricted supermodule category for gl（m｜n） are presented.
基金Project supported by the National Natural Science Foundation of China and Beijing Natural Science Foundation.
文摘A generalized first Noether theorem (GFNT) originating from the invariance under the finite continuous group for singular high-order Lagrangian and a generalized second Noether theorem (or generalized Noether identities (GNI)) for variant system under the infinite continuous group of field theory in canonical formalism are derived. The strong and weak conservation laws in canonical formalism are also obtained. It is pointed out that some variant systems also have Dirac constraint. Based on the canonical action, the generalized Poincaré-Cartan integral invariant (GPCⅡ) for singular high-order Lagrangian in the field theory is deduced. Some confusions in literafure are clarified. The GPCⅡ connected with canonical equations and canonical transformation are discussed.
