黎曼几何

在黎曼几何中，带有左不变黎曼度量的幂零和可解李群具有重要作用。如：它们出现在非紧致黎曼对称空间的等距群的Iwasawa分解中；

Nilpotent and solvable Lie groups with left-invariant Riemannian metrics play a remarkable role in Riemannian geometry .

曲率是黎曼几何中的热门研究课题。

Positive curvature has been a frequent subject in Riemannian geometry .

傍轴黎曼几何光学Ⅲ.光束传输的统计行为

Paraxial Riemannian Geometrical Optics ⅲ . Statistical Behaviors of Beam Propagation

傍轴黎曼几何光学.Ⅳ.两种光束质量因子

Paraxial Riemannian Geometrical Optics ⅳ . Two Kinds of Beams Quality Factors

伍鸿熙等著，《黎曼几何选讲》，北京大学出版社。

J.Cheeger , Comparison Theorems in Riemannian Geometry , North-Holland publishing company .

无风险控制的log-最优投资组合问题的一个黎曼几何随机算法

An Riemannian Geometry Underlying Stochastic Algorithm for the Risk-free log-Optimal Portfolio Problem

傍轴黎曼几何光学&V.傍轴光束的空间变换

Paraxial Riemannian Geometrical Optics V. Space-Transform of Paraxial Beams

关于黎曼几何中的法圆公理

On the axiom of normal circles in Riemannian manifold

傍轴黎曼几何光学.&Ⅱ.应用基础

Paraxial Riemannian Geometrical Optics . ⅱ . Basic Applications

黎曼几何在并联机构动力学中的应用

Applications of riemannian geometry on parallel mechanisms dynamics

傍轴黎曼几何光学·Ⅰ理论

Paraxial Riemannian Geometrical Optics ⅰ . Theory

而张量分析与黎曼几何的深入发展，极大地促进了现代数学的进步。

Moreover , tensor analysis and Riemannian geometry developed deeply which promotes modern math development further .

利用黎曼几何等工具研究了一般并联机器人的动力学建模和跟踪控制的一般化方法。

Using the Riemannian geometry language , the modeling and control of general parallel robots are studied .

本文对牛顿万有引力定律提出了一种非黎曼几何的相对论性的可能修正公式。

In this paper , a possible Correction of non-Riemannian geometric relativity is made for Newton 's Law of Gravitation .

自黎曼几何诞生以来，黎曼流形的研究一直成为黎曼几何研究的核心内容。

The study on the Riemannian manifold is an important field of the Riemannian geometry since Riemannian geometry had been born .

但艾伦和莱夫谢茨的交往，仅仅是莱夫谢茨问他能否听懂L.P.艾森哈特的黎曼几何讲座，而艾伦则认为这个问题非常无礼。

but Alan 's personal contact with him was probably characterised by an occasion when Lefschetz questioned whether he would understand L.P. Eisenhart 's lecture course on Riemannian geometry , a question Alan considered insulting .

主要研究了一大类p-调和映照的p-能量增长性质，利用黎曼几何中Hessisn比较定理，得到了关于p-能量增长的特殊估计。

In this paper , we study the p-energy growth property for a large class of p-harmonic maps . Using Hessian comparison theorem in Riemannian geometry , we obtain the special estimation of p-energy growth .

当变系数只依赖于空间变量时，我们用距离函数构造几何乘子，然后用黎曼几何中经典的比较定理来估计余项。

If the coefficients depend only on the spatial variable , we use the distance function to construct the multiplier , and then use the classical comparison theory from Riemannian Geometry to deal with the error terms .

但是，外尔的这些工作是从黎曼几何过渡到纤维丛理论的一个重要环节，同时也是外尔从分析学转向李群理论的主要动因。

But the author argues that Weyl 's work in this field is not only an important historical linkage from Riemann geometry to fiber bundle but also a main incentive for his research diversion from analysis to Lie group .

本文讨论了变系数波方程振动传递的边界镇定，应用黎曼几何方法和迹的正则性得到了所讨论问题的能量一致衰减率。

The aim of this paper is to study the boundary stabilization of the transmission of wave equations with variable coefficients . The uniform energy decay rate for the problem is established by Riemannian geometry methods and sharp trace regularity .

黎曼几何诞生于德国数学家B.Riemann的著名的就职演说论作为几何学基础的假设，后经许多著名数学家的进一步完善和推广，成为一门重要的数学理论。

Riemannian geometry started from the famous speech " On the hypothesis as the foundation of geometry " of the German mathematician B. Riemann , it became into an important mathematics theory after the improvement and generalization of many famous mathematician .

黎曼几何的研究从局部发展到整体，产生了许多深刻的并在其它数学分支，如代数拓扑、偏微分方程、多复变函数论等以及现代物理学中有重要作用的结果。

The investigation of Riemannian geometry , from localization to globe , produced many important results , which can be used in many mathematical fields such as algebra topology , partial differential equation , multiple valued complex analysis as well as modern physics .

黎曼的几何思想及其对相对论的影响

Riemann 's Idea of Geometry and its Impact on the Theory of Relativity

黎曼的几何思想萌芽

The Rudiments of the Idea of Riemann for Geometry

完备黎曼流形的几何性质

The Geometry of a complete Riemannian manifold

一个像黎曼这样的几何学者几乎可以预见到现实世界的更重要的特徵。

In this paper , we use the method of the estimated characteristic function to estimate a lower bound of the first eigenvalue on compact Riemann manifold .

利用Jacobi场、Rauch比较定理、核心等概念和定理讨论了完备黎曼流形的若干几何性质。

In the paper , we discuss the geometry of a complete Riemannian manifold by the concepts and theorems of Jacobi field 、 Ranchs Comparison Theorem and Soul etc.

图的Laplace矩阵与二阶微分算子Laplacian之间的紧密联系使得在黎曼流形的谱几何与图论之间建立了一个重要的双向联系。

Laplace matrices of graphs are closely related to the Laplacian , the second order differential operator . This relation yields an important bilateral link between the spectral geometry of Riemannian manifolds and graph theory .

某些局部对称黎曼流形的谱几何

The spectral geometry of some locally symmetric manifolds

黎曼流形是黎曼几何的主要研究对象，黎曼流形的曲率与拓扑以及M（？）

Riemannian manifold is the studying object of Riemannian geometry .