黎曼空间

其间，导出了其壳体黎曼空间中的Green－Lagrange应变张量和第二类Piola－Kirchhoff应力张量的表达形式，并通过虚功原理，建立了薄壳结构的非线性平衡关系。

Also derived in the paper are the Green-Lagrange strain tensor and the second Piola-Kirchhoff stress tensor in the Riemann space of the shell . Finally , on the basis of the virtual work , the non-linear equilibrium equations of thin-shell structures are developed .

关于黎曼空间的切纤维丛主丛与刚体运动

ON THE BUNDLES OF ORIENTED m-PLANES OF A RIEMANN SPACE . Principal Fibre Bundle and Motion of Rigid Body

关于可容纳n重正交极小超曲面系统的黎曼空间Vn

On the riemannian spaces Vn which admit an n-tuply orthogonal system of minimal hypersurfaces

如所知，拟常曲率黎曼空间等价于共形平坦的拟Einstein空间。

As is well known to us , a quasi-constant curvature Riemannian space is equivalent to a conformally flat quasi - Einstein space .

n-2型黎曼空间的等距对应

D shape . on the isometric correspondence of Riemannian Spaces of category n & 2

研究伪黎曼空间型的2-调和类空子流形，通过计算，获得了这种子流形上一个Simons型积分不等式。

2-Harmonic space-like submanifolds in a pseudo-Riemannian space form was studied , and a Simons form inequality of integration was obtained via calculations .

A.Einstein把引力现象解释成黎曼空间的曲率性质，使得物理现象变成几何现象，从而使黎曼几何在广义相对论和理论物理中得到了广泛的应用。

A. Einstein took the gravitation phenomenon as the curvature property of Riemannian space , the physics phenomenon may be considered as geometry phenomenon . Therefore , Riemannian geometry may be applied in general relativity theory and theoretical physics .

黎曼空间等价问题的讨论

A discussion on the problem of the equivalent of Riemannian Spaces

关于拟常曲率黎曼空间的循环超曲面

On the Recurrent Hypersurfaces in a Riemannian Space with Quasi-constant Curvature

关于非正定的黎曼空间中的运动群

On groups of motions in a Riemannian space with indefinite metric

容有全脐超曲面族的某些黎曼空间

On Some Riemannian Spaces Admitting Family of Totally Umbilical Hypersurfaces

伪黎曼空间型中子流形几何的若干问题

Some Problems on Geometry of Submanifolds in Pseudo-Riemannian Space Forms

拟常曲率黎曼空间的某些性质

On some properties of Riemannian space of quasi-constant curvature

关于线素非正定的黎曼空间的共形变换群

On the Group of Conformal Transformations of a Riemannian Space with Indefinite Metric

关于拟常曲率空间与某些黎曼空间

On Quasi-Constant Curvature Spaces and Some Riemannian Spaces

伪黎曼空间型的2-调和类空子流形

2-Harmonic Space-like Submanifolds in a Pseudo-Riemannian Space Form

盲源分离的常规随机梯度算法只适用于欧氏空间，对于更一般的黎曼空间则必须采用自然梯度算法。

Standard stochastic gradient algorithm of blind source separation is only adapted to Euclidean space .

非黎曼空间测地逼近及其在电力系统非线性自适应控制中应用

Geodesic Approaching in Non-Riemannian Space and Its Application to Adaptive Non-linear Control Design in Power systems

关于共形对应黎曼空间的一点注记

Some Notes on Conformal Riemannian Spaces

自然梯度下降法是一种新的最优化方法，自然梯度下降法是在黎曼空间下提出的，自然梯度相比于标准梯度有很多优点。

Natural gradient is a new optimization way that is proposed in a special space ? Riemannian Space .

它进一步说明一个四元流形的截面曲率的估计对许多对称黎曼空间都是有效的。

It proves that the estimate sectional curvature of a quaternion manifold is very useful for Riemann symmetric space .

本文研究了伪黎曼空间型中具有常平均曲率的类空子流形，得到了这类空子流形的一个积分不等式及刚性定理。

This paper discusses the space-like submanifolds with constant mean curvature in a pseudo-Riemannian space form , and obtain an integrate inequality and a rigidity theorem .

本文定义了伪黎曼空间型中的旋转超曲面，并给出其参数表达式及主曲率计算公式。

Rotation hypersurfaces in pseudo-Riemannian space forms are defined and their explicit parametrizations are given in the present paper , and their principal curvatures are computed .

李三系源于微分几何中黎曼对称空间、全测地流形；

Lie triple systems arose initially in studies of Riemannian geometry ;

利用黎曼对称空间同正交对称李代数之间的密切关系及一个矩阵不等式给出了一个复流形上截面曲率的上界的精确估计。

We used the relationship of the Riemann symmetric space and the symmetric algebra , a matrix inequality to provided a estimate sectional curvature of a complex manifold .

通过计算全测地子流形的基本群，确定了紧正规黎曼对称空间的极大的极大秩全测地子流形的整体分类。

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 .

紧致黎曼4-对称空间的Cartan嵌入

Cartan Embeddings of Compact Riemannian 4 - Symmetric Spaces

利用活动标架，得到关于Finsler空间的一些基本公式和结果，并研究了具有退化黎曼曲率的Finsler空间的几何。

By moving frames , the basic formulas and some results on a Finsler space ( M , F ) and geometry of Finsler spaces with vanishing Riemann curvature are studied .

给出了一类黎曼浸没在全空间中第一特征值的下界估计。

The lower bound of the first eigenvalue on compact Riemann manifold ;

李奇曲率平行的黎曼流形到欧氏空间的等距浸入

On Isometric Immersion of a Riemannian Manifold with Parallel Ricci Curvature Into Euclidean Space