黎曼流形 的英文怎麼說
中文拼音 [límànliúxíng]
黎曼流形
英文
riemann manifold-
This paper deals with the regular curves in a riemannian manifold with constant sectional curvature and the affine starlike curves in r2, r3 and r4
本文研究了具有常截面曲率的黎曼流形中的正則曲線及二、三、四維空間中的仿射星形曲線。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The complete open nonnegatively curved riemannian manifolds with souls of codimension one
核心的余維數為1的具非負曲率完備非緊黎曼流形Maximal and minimal value principle of differentiable functions on noncompact complete riemannian manifold
非緊完備黎曼流形上可微函數的極值原理The second part consist of chapter four. in chapter one, we study the energy density of harmonic map from finsler manifold and generalize classical result in [ se ]. in chapter two, we obtain lower estimates for the first eigenvalue of the laplace operator on a compact finsler manifold, and it generalize lichnerowicz - obata theorem [ li ] [ ob ]. in chapter three, we derive the first and second variation formula for harmonic maps between finsler manifolds. as an application, some nonexistence theorems of nonconstant stable harmonic maps from a finsler manifold to a riemannian manifold are given
第一章討論finsler流形到黎曼流形調和映射的能量密度的間隙性，推廣了[ se ]中的結果。第二章對緊致finsler流形上laplace運算元的第一特徵值的下界作了估計，推廣了黎曼流形上的lichnerowicz - obata定理[ li ] [ ob ] 。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。Suanifolds with the vanishing normal curvature tensor in locally syetric space
局部對稱黎曼流形中法曲率張量場消失的子流形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 complete hypersurfaces with constant mean curvature in locally symmatric manifold are investigated, a characteristric theorem of complete hypersurface in locally symmatric manifold is obtained
摘要研究局部對稱黎曼流形中的具有常中曲率的完備超曲面，得到了這類曲面全臍的一個結果。One of open problems is to study harmonic maps between finsler manifolds and derive the first and second variation formula for harmonic maps between finsler manifolds. firstly, we define harmonic map between finsler manifold. in fact, it is the harmonic map from projective sphere bundle of source manifold to the projective sphere bundle of target manifold
運算元的第一非零特徵值凡全mk .特別地，當『 ，二二k時， m的直徑為六?當m是黎曼流形時，由moer 「定理的推論直接可知m與半徑為去的球等距On submanifolds with parallel mean curvature in a riemannian manifold of quasi constant curvature
擬常曲率黎曼流形中具有平行平均曲率向量的子流形On the submanifolds with parallel mean curvature in a eiemannian manifold of quasi constant curvature
擬常曲率黎曼流形中具有平行平均曲率向量的子流形Curvature tensor of riemannian manifold
關于黎曼流形的曲率張量Complete riemannian manifold
完備黎曼流形Moments of hitting time of geodesic sphere by brownian motion on riemannian mannifolds
黎曼流形上布朗運動關于測地球擊中時的矩Submanifolds with flat connection of normal bundle in a riemannian manifold of quasi constant curvature
擬常曲率黎曼流形中的法聯絡平坦子流形Estimations of the moments of the hitting time by brownian motions on general riemannian manifolds are also obtained
估計了一般黎曼流形上的布朗運動關于球面擊中時的各階矩。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 compact minimal submanifold of a locally symmetric and conformally flat riemannian manifold are studied, and obtain the following intrinsic rigidity theorem. i. e. if m be a compact minimal submanifold of a locally symmetric and conformally flat riemannian manifold n ( superscript n + p )
摘要研究了局部對稱共形平坦黎曼流形的緊致極小子流形，即設m是局部對稱共形平坦黎曼流形的n維緊致極小子流形，得到了這種子流形的若干內蘊剛性積分不等式，給出了流形全測地的限制條件。In this paper, the authors give the globally classfication of the maximal totally geodesic submanifolds with maximal rank of normal riemannian symmetric spaces by computing the fundamental group
摘要通過計算全測地子流形的基本群，確定了緊正規黎曼對稱空間的極大的極大秩全測地子流形的整體分類。分享友人