Riemann curvature tensor

The Riemannian metric of perspective in stereo graphic projection is introduced and a property of the continual cut vector field on the spherical surface is discussed.

介绍了在球极投影下引入的黎曼度量,并介绍了这种度量的一些性质,指出了这种度量与从平直的欧几里德空间标准度量中诱导的黎曼度量是一致的;同时指出在球面上的连续切向量场上必然有奇点存在,这就为球面的量测作了理论上的准备;最后介绍了球极投影下的联络系数及其计算公式。

We deduce the Riemannian metric on complex projective space from Riemannian submersion π:S2n+1→CPn,get its volume element We also prove that one type totally real submanifolds of CPn is none but ndimensional sphere Sn.

用黎曼淹没π：Ｓ２ｎ＋１→ＣＰｎ诱导出ＣＰｎ上的黎曼度量及其在不同坐标系下的表达形式；算出其体积元，并得到ＣＰｎ上一类ｎ维全实子流形与ｎ维球面Ｓｎ等

In this paper, we study some conditions and properties for an important class of randers metrics in forms of F(y)=(β(y)~2+(1-|β|~2)α(y)~2)~(1/2)-β(y)/1-|β|~2 to be pointwiseprojective toα,whereα(y)=(α_(ij)(x)y~iy~j)~(1/2) is a Riemannian metric on ann-dimensional manifold M andβ(y)=b_i(x)y~i is a 1-form on M.

本文研究了一类重要的形如F(y)=(β(y)~2+(1-|β|~2)α(y)~2)~(1/2)-β(y)/1-|β|~2的Randers度量与黎曼度量α逐点射影相关的条件和性质。

Face Illumination Modeling Method Based on the Face Image Multimode Decomposition of Riemannian Tensor

基于黎曼张量的人脸图像多模态分解光照建模方法

contracted Riemann-Christoffel tensor

缩并的黎曼－克列斯托弗张量

At the same time, The curvature tensor expression of a Riemannian manifold under the special semi-symmetric metric-recurrent connections is also obtained.

同时给出了特殊半对称联络的黎曼流形曲率张量表示。

Douglas Metrics with Some Non-Riemannian Curvature Properties

具有某些非黎曼曲率性质的Douglas度量

(α,β)-Metrics of Certain Important Non-Riemann Curvature Properties;

具有某些重要非黎曼曲率性质的（α，β）-度量

Hynersurface with Constant Sclar Currature in QC Riemannian Manifold;

常QC黎曼流形中具有常数量曲率的超曲面

Existence of Solutions to Weak Vector Variational-Like Inequalities on Riemannian Manifolds

黎曼流形上弱向量似变分不等式解的存在性

Study on the Magneto-Photovoltaic and the Hyper-Raman Tensors of Crystals

晶体磁光生伏打张量和超拉曼张量的研究

THE HARMONIC MAPS FROM RIEMANIAN MANIFOLD INTO PSEUDO RIEMANNIAN MANIFOLD (Ⅰ)

黎曼流形到伪黎曼流形的调和映照(Ⅰ)

On Exponential Metrics with Isotropic S-Curvature and Finsler Metrics Which Are Projectively Equivalent to a Riemann Metric;

关于具有迷向S-曲率的指数度量及与黎曼度量射影相关的Finsler度量

Some Properties of a Class of Randers Metrics is Pointwise Projective to Riemannian Metric;

一类重要的Randers度量与黎曼度量逐点射影相关的性质

Some Non-Riemannian Curvature Properties of the Douglas Metrics and the Finsler Metrics of Randers Type

Douglas度量及Randers型芬斯勒度量的若干非黎曼曲率性质

The projective trans for mation of semi-symmetric metric-recurrent connections on a Riemannican manifold is discussed.

讨论了黎曼流形上半对称度量循环联络的射影变换。

Finite Determination with Respect to R-equivalence from the Weighted Point of View and Its Criterion;

奇异黎曼度量下光滑函数芽的右有限决定性及其判定

Submanifolds with parallel mean curvature vector in pinched riemannian manifolds;

Pinched黎曼流形中具有平行平均曲率向量的闭子流形

The Submanifolds with Parallel Mean Curvature Vector in A Locally Symmetric Riemannian Manifold;

局部对称黎曼流形中具有平行中曲率向量的子流形

The compact pseudo-umbilical submanifold with parallel mean curvature vector in the Riemannian manifold with constant curvature

常曲率黎曼流形中具有平行中曲率向量的紧致伪脐子流形

On submanifolds with parallel mean curvature in a locally symmetric quasi-constant curvature Riemannian manifold

局部对称拟常曲率黎曼流形中具有平行平均曲率向量的子流形