tangent manifold 中文意思是什麼
tangent manifold
解釋
切流形-
Harmonic maps between riemannian manifolds are very important in both differential geometry and mathematical physics. riemannian manifold and finsler manifold are metric measure space, so we can study harmonic map between finsler manifolds by the theory of harmonic map on general metric measure space, it will be hard to study harmonic map between finsler manifolds by tensor analysis and it will be no distinctions between the theory of harmonic map on finsler manifold and that of metric measure space. harmonic map between riemannian manifold also can be viewed as the harmonic map between tangent bundles of source manifold and target manifold
黎曼流形間的調和映射是微分幾何和數學物理的重要內容。黎曼流形和finsler流形都是度量空間，自然可利用一般度量空間調和映射的理論討論finsler流形間的調和映射。但由於控制finsler流形性質的各種張量一般情況下很難應用到一般度量空間調和映射的理論中，使得這樣的討論大都是形式上的，並與一般度量空間調和映射的理論區別不大。 -
In this paper, we introduce the definition of lie bialgebroid and its dirac structures firstly. then we particularly discuss the tangent lie bialgebroid, based on the conclusion and thorems given by a. weinstein, z - j., liu. in section two, we study the nijenhuis tensor, which causes the deformation of poisson tensor. view poisson - nijenhuis manifold as a special case of bihamiltonian manifold, we will show some special anduseful properties of poisson - nijenhuis manifold
將poisson - nijenhuis流形作為雙hamilton流形的一個特例，得到poisson - nijenhuis流形上一些比較特殊和有用的性質；並給出了poisson - nijenhuis流形上的形變李代數胚和形變李雙代數胚。
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