黎曼幾何 的英文怎麼說
中文拼音 [límànjīhé]
黎曼幾何
英文
riemannian geometry-
In this papaer, a note about the proof of the chain rule in the book 《 an introduction to differentiable manifolds and riemannian geometry 》 is offered
給出了《微分流形與黎曼幾何引論》一書中關于鏈法則證明的一個注記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。Also, general relativity defines non - inertia space - time as a space of riemann. for riemann space has positive curvature, we have to doubt about where the minus curvature space is
廣義相對論把非慣性時空定義為黎曼空間，但由於黎曼幾何是正曲率空間，既然廣義時空是對稱的，我們必然要問，負曲率空間到哪去了？When target manifold is r, . if u is a function of finsler manifold, we can define laplace operator, it is well - defined. if u is called the eigenvalue of the laplacian a and u is called the corresponding eigenfunction
眾所周知，對于黎曼幾何，調和映射是調和函數的推廣，且當目標流形為r時，二（喲二撇el ] .因此對于屍『 nsler流形m上的函數。可以定義laptace運算元為。The text however develops basic riemannian geometry, complex manifolds, as well as a detailed theory of semisimple lie groups and symmetric spaces
然而課程還將簡單介紹了基本的黎曼幾何和復流形的知識，並會詳細討論半單李群和對稱空間的理論。The non - riemannian geometric quantities in finsler geometry describe the difference between finsler geometry and riemann geometry
Finsler幾何中的非黎曼幾何量刻畫的是finsler幾何與黎曼幾何的不同之處。The text for this class is differential geometry, lie groups and symmetric spaces by sigurdur helgason ( american mathematical society, 2001 )
然而課程還將簡單介紹了基本的黎曼幾何和復流形的知識，並會詳細討論半單李群和對稱空間的理論。A riemannian geometry underlying stochastic algorithm for log - optimal portfolio problem with risk control
最優投資組合問題的一個黎曼幾何隨機演算法A riemannian geometry underlying stochastic algorithm for adaptive principal component analysis
主成分分析的一個黎曼幾何隨機演算法The basic idea to construct grpcs is to establish object topology first, then use geometry to change the shape of differential manifold. in chapter 2, we discuss the theoretical framework of grpcs that includes some relative idea about differential manifold. firstly, the definition of potential function on manifold is given
本文首先討論了廣義有理參數曲線曲面的理論基礎，依次闡述了黎曼幾何中關于流形、函數和映射的基本概念，並在此基礎上提出了微分流形上勢函數的定義。分享友人