riemannian space 中文意思是什麼
-
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。 -
Its content may be separated into two parts. the first part contains chapter one and chapter two, which treat of the harmonic maps from surface into symplectic groups and quaternion grassmann manifolds. the second part contains chapter three and chapter four, which treat of local isometric immersions from space forms or riemannian products of space forms into space forms
全文分四章，內容可分為兩部分：第一部分包括第一、二章，主要論涉從曲面到辛群及四元grassmann流形的調和映射；第二部分包括第三、四章，主要論涉從空間形式或空間形式的局部riemann積到空間形式的局部等距浸入。 -
Natural gradient is a new optimization way that is proposed in a special space ? riemannian space. the parameter space in blind source separation is riemannian space. natural gradient has many better characters compared with normal gradient
自然梯度下降法是一種新的最優化方法，自然梯度下降法是在黎曼空間下提出的，自然梯度相比于標準梯度有很多優點。
分享友人