查询词典 Riemannian

Modern geometry has multiple strong bonds with physics , exemplified by the ties between Riemannian geometry and general relativity .

自十九世纪以来发现非欧几里德几何，空间的概念，经历了一个彻底转变。

Riemannian normal coordinates contain information about the direction and distance from a specific point on a manifold to other points nearby. It is worth to translate this technique from its original setting in differential geometry, to the task of manifold learning.

黎曼正则坐标包含了流形中指定点到邻近点的方向和距离信息，如何将这种源于微分几何的技术应用到流形学习中也是值得研究的课题之一。

We prove that an n-dimensional complete open Riemannian manifold M with Ricci curvature Ric_M ≥ 0 is diffeomorphic to an Euclidean n-space if M satisfies some volume growth conditions.

第二章，我们研究了Ricci益率有一定下界的完备非紧n维Riemann流形，证明了这样的流形在满足一定体积增长条件下微分同胚于n维欧几里德空间。

And resolves many difficult issues for complex multibody systems dynamic analysis, design and simulation in engineering areas. Therefore, it is worth to deeply investigate and perfect the spatial operator algebra.

本篇论文也是以空间算子代数理论为研究对象，对其理论作深入研究，并在Lie群、Lie代数、Riemannian流形理论体系中建立空间伴随算子形式的高效率建模和高效率递推运算动力学模型。

In particular, rotation hypersurfaces of finite type are studied and classified. The existence of rotation hypersurfaces with prescribed principal curvature functions in pseudo-Riemannian space forms is proved.

对有限型旋转超曲面进行了研究，得到分类结果；证明了给定主曲率函数的旋转超曲面的存在性。

Let be an n dimensional Riemannian manifold, the properties of harmonic functions on it are the interesting problems in geometric analysis.

在黎曼流形上的分析中，很大一部分是对流形上函数的调和性研究[1 - 2 ] ，并从中得到关于这些函数的性质。

Secondly,for nonlinear vibratory systems,the relationship between a class of stationary geodesics of the Riemannian manifold and the nonlinear normal modes is found.

进而，将类似的对应关系推广应用到非线性振动系统中，得到了非线性模态与 Riemann 流形上的极值测地线之间的对应关系。

The spectrum of the Laplacian on a Riemannian manifold is an importantanalytic invariant and is deeply connected with geometry and topology of a man-ifold.

黎曼流形上Laplace算子的谱是流形上重要的解析不变量，它与流形的几何、拓扑有着深刻的联系。

The paper discusses the structure of the soul in a complete noncompact Riemannian manifold M with nonnegative curvature,and proves that if the soul of the manifold is unique,then the soul actually degenerates to a pole.

讨论了具非负曲率的完备非紧黎曼流形上的核心的结构，证明了如果核心是惟一的，那么核心将退化为极点。

2The new cloud physical model is put forward the metric geometry.(3)The generalized cloud equations of cloud is derived on the generalized function and the Sobolev space on the Riemannian manifold.

提出了 大气模式中新一代云方案的动力学：(1)基于拓扑的云分类；(2)基于度量几何的云模型(3)利用黎曼流型上的广义函数和索伯列夫空间，系统建立了云之动力学方程组。

On the other hand, the more important thing is because the urban housing is a kind of heterogeneity products.

另一方面，更重要的是由于城市住房是一种异质性产品。

Climate histogram is the fall that collects place measure calm value, cent serves as cross axle for a few equal interval, the area that the frequency that the value appears according to place is accumulated and becomes will be determined inside each interval, discharge the graph that rise with post, also be called histogram.

气候直方图是将所收集的降水量测定值，分为几个相等的区间作为横轴，并将各区间内所测定值依所出现的次数累积而成的面积，用柱子排起来的图形，也叫做柱状图。