黎曼度量

统计流形在一定的不变原则下被证明具有唯一的黎曼度量，即为Fisher信息阵，以及一对对偶的仿射联络。

Under the invariance principle , the manifold is proved to have a unique Riemannian metric given by the Fisher information matrix , and a dual pairs of affine connections .

讨论了FisherZ分布流形的对偶结构及其平坦性，进而给出了该流形的黎曼度量、α仿射联络和α曲率，并在该统计流形上定义了散度来衡量两点之间的距离；

A dual affine structure is constructed on it and a divergence is defined as a distance like measure . Furthermore , the Riemannian metric , α - connections and α - curvatures of the Fisher Z manifold are given .

在Delaunay三角剖分算法的基础上，通过引入黎曼度量矩阵完成了曲面非结构网格生成，并给出了黎曼空间下的近似外接圆准则。

Based on the algorithm of Delaunay triangulation , introduce a metric tensor to complete the surface triangulation . And the definition of the cavity in a Riemannian space is given .

针对PCA、ICA特征提取方法，基于微分几何的数学理论，综合考虑了雷达目标距离像识别中的特征提取与分类识别，提出基于黎曼度量的最近中心邻分类器。

Put forward Riemannian metric-based nearest center neighbor classifier ( RMNCC ) on the basis of differential geometry , correlating the feature extraction based on PCA and ICA and classification in radar target recognition on the foundation of mathematics .

我们主要是来证明，那些非紧型的Hermitian对称空间恰恰就是C~n中的对称有界域，其上的黎曼度量由Bergman度量给出，以及对不可约Hermitian对称空间的刻画。

Our main goal is to prove that those of noncompact type are exactly the bounded symmetric domains in C ~ n with Riemannian structure given by the Bergman metric , and to characterize the irreducible Hermitian symmetric spaces .

在各向同性算法中引入黎曼度量表征单元尺寸，计算两点距离，获得黎曼度量场下的Bowyer-Watson增量插点内核，实现平面各向异性Delaunay网格生成。

Riemannian metric is introduced to define mesh sizes and to calculate point-to-point distances , thus a traditional isotropic Bowyer-Watson kernel for Delaunay mesh generation is revised for Riemannian context of planar anisotropic mesh generation .

认为曲面的共形参数化过程等价于寻找一个合适的黎曼度量，使得该度量和网格的初始度量共形等价，并且它所诱导的Guass曲率在内部点处为零。

We think that conformal surface parameterization is equivalent to finding a proper Riemannian metric on the surface , such that the metric is conformal to the original metric and induces zero Gaussian curvature for all interior points .

奇异黎曼度量之下的分支问题的d-充分性

D - sufficiency of bifurcation problems under singular Riemannian metric

基于黎曼度量的复杂参数曲面有限元网格生成方法

Surface Mesh Generation Based on Riemannian Metric

纤维丛的黎曼度量

The Riemannian metric of fiber bundles

详细阐述了曲面参数域上任意一点的黎曼度量的计算和插值方法；

The calculation and interpolation method of arbitrary points in surface 's parametric space are detailed .

反之，对于紧致拓扑流形，能否由基本群决定在它上面是否容许有非正曲率的黎曼度量？

Can the fundamental groups of any compact topological manifold determin that it admits a non-positively curved Riemannian metric ?

最后，应用近似化方法和黎曼度量方法，研究了机器人最优轨迹规划的问题。

In the end , the problem of robot trajectory planning is investigated by the linearization method and Riemannian metric .

针对映射法容易产生畸变而导致网格质量较差的问题，提出了一种黎曼度量和前沿推进技术相结合的曲面网格生成方法。

However , mapped method tends to generate distortion elements , which leads to poor quality meshes . Based on mapped method , the Riemannian metric was applied .

如何从纤维丛的底空间和纤维型的黎曼度量构造丛空间的黎曼度量，接着，定理1和定理2分别给出了向量丛和主丛关于这种度量的线素。

A new definition concerning the Riemannian metric of bundle spaces is given by using of the Riemannian metric of related base spaces and fibers . Theorem 1 and theorem 2 give the line elements of the metric for the vector bundles and for the principal bundles , respectively .

黎曼流形上度量的Ricci流的一个定理

A theorem of Ricci flow of metric on Riemannian manifold

HCMU度量是黎曼曲面上极值度量的一个退化情形，具有整体旋转对称性。

HCMU metric is a special kind of extremal metric on Riemannian surface with global rotational symmetric .

基于二维倒立摆，构造倒立摆的能量函数，以能量优化为目标把能量函数映射成黎曼曲面，推导出黎曼度量矩阵。

Based on the 2D-inverse pendulum , build the energy equation , and take the least energy as target to change the equation into Riemann surface , then derive Riemann measure matrix .

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 .