查询词典 Riemannian

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。

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。

The n-dimensional umbilical submanifolds in a Riemannian manifold of quasi constant curvature are discussed.

摘要讨论拟常曲率黎曼流形中的全脐子流形，得到关于这类子流形的两个定理。

This paper is divided two chapters. The first chapter discusses the existence and uniqueness of solution for the Cauchy problem of the following quasilinear degenerate parabolic equationThe second chapter studies the geometric properties of a Riemannian manifold.

本文分两部分，第一部分是对如下形式的拟线性退化抛物方程Cauchy问题讨论了解的存在唯一性；第二部分是讨论了黎曼流形中的一些几何问题，主要是将欧氏空间平行射线的概念推广到一般黎曼流形，并研究其所具有的性质。

We get some results about the scalar curvature of 2 and n(n≥3)dimensions Einstein manifold :ρ Maybe is constant and ρ is constant, the relation between Einstein Manifold and Riemannian Manifold with constant sectional curvature.

本文对其有关性质进行了讨论，得到了2维和n(n≥3)维爱因斯坦流形的数曲率的一些结果：ρ可能为常数和ρ为常数，以及爱因斯坦流形与常曲率黎曼流形之间的关系

The network space is the typical form of abstract space when it comes to the digital stage.

网络空间是抽象空间数字化阶段的典型形式。

The Notarial System,as the system of judicial certification in our country,is both the constructor and the defender of social credit system,It has its special value and function in the social honesty.

公证制度作为我国司法证明制度，既是社会信用体系的建设者，同时也是社会信用的捍卫者，在诚信中有其特殊的价值和功能。