查询词典 manifolds

Geometry of Manifolds analyzes topics such as the differentiable manifolds and vector fields and forms.

流形上的几何学讨论的问题是微分流形，向量场和微分形式。

At the most basic level, this course gives an introduction to the basic concepts of differential manifolds, exterior differentiation and Riemannian manifolds.

本课程主要介绍微分流形的基本概念和例子、外微分以及黎曼流形的初步知识。

Finally, we get local stable manifolds and local unstable manifolds of near hyperbolic equilibrium point of nonlinear autonomous dynamical systems by the properties of bounded solutions to nonlinear nonautonomous equations.

最后运用非线性非自治中立型泛函微分方程有界解的性质，得到非线性自治动力系统在双曲平衡点的局部稳定流与局部不稳定流。

Finally,we get local stable manifolds andlocal unstable manifolds of near hyperbolic equilibrium point of nonlinearautonomous dynamical systems by the properties of bounded solutions to nonlinearnonautonomous equations.

最后运用非线性非自治中立型泛函微分方程有界解的性质，得到非线性自治动力系统在双曲平衡点的局部稳定流与局部不稳定流。

In this paper, we consider neutral functional differential equations and study the global existence of their solutions, stable subspaces and unstable subspaces of linear autonomous dynamical systems, local stable manifolds and local unstable manifolds of near hyperbolic equilibrium point of nonlinear autonomous dynamical systems, periodic solutions and oscillation of the neutral equations.

本文主要研究中立型泛函微分方程解的整体存在性，自治线性动力系统的稳定子空间与不稳定子空间、自治非线性动力系统在双曲平衡点的局部稳定流与局部不稳定流，周期解与解的振动性。

The Laplacian on Riemannian manifolds is an essential linear operator, and it is also the main object to be studied of Geometric Analysis on manifolds.

Riemann流形上的Laplace算子是一个重要的线性算子，也是流形上几何分析研究的主要对象之一。

It is also considered to study the Finsler geometry which deal with the Chern''s connection、flag curvature、Ricci scalar of Finsler manifolds、Finsler submanifold geometry, and harmonic maps between Finsler manifolds.

研究芬斯勒几何的某些问题，包括芬斯勒流形的陈省身联络、旗曲率、Ricci数量、芬斯勒子流形几何以及芬斯勒流形间的调和映射等。

In chapter 4,we consider the existence of harmonic function in negative sectional curvature manifolds.we get that,if Ricci ≥-C(1 + r~2)r =ρ(O.x, then there have non-canstant bounded harmnic function in negative sectional curvature manifolds.

第四章考虑负曲率流形上调和函数，得到了在Ricci≥-C(1+r~2)其中r=ρ的负曲率流形的调和函数的存在性。

Besides,we study the topology of Riemannian manifolds with some curvature conditions via comparisonsl geometry methods,and we get some results towards the topological type and the finiteness of isomorphism classes of fundamental groups of some Riemannian manifolds.

另外，我们在比较几何的框架下研究了具特定曲率条件的Riemannian流形的拓扑，得到了有关有限拓扑型和基本群同构类的一些结果。

Shen prove a short time existence theorem for manifolds with umbilical boundary. He also derived the Simons' identity for the boundary under the Ricci flow. And as a corollary, Shen show that any three-manifolds with totally geodesic boundary which admits positive Ricci curvature can be deformed to a space form with totally geodesic

而带边流形上的Ricci流的研究始于Shen，在1996年，Shen在中考虑带边三维流形上的黎曼度量的Ricci形变，证明了如果初始三维流形的黎曼度量具有正Ricci曲率和全测地边界，则此三维黎曼流形上存在着常正曲率的黎曼度量。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。