查询词典 manifolds

By using it, we solve the Yamabe problem on quaternionic contact manifolds when the Yamabe invariant is smaller than that of the sphere.

我们还建立了四元切触流形的分析基础，应用建立的分析工具，在流形Yamabe不变量与球面的不同时，解决了四元切触流形上的Yamabe问题。

In the first chapter, we study the metric deformation on Riemannian manifolds with boundary.

在第一章中，我们讨论了高维带边黎曼流形上的Ricci流。

In chapter 2,we study complete noncompact Riemannian manifolds with nonegative Ricci curvature.

在第一章，我们对涉及本文研究领域的有关流形曲率与拓扑关系的研究现状作了简单的阐述。

This paper describes objects by Riemannian manifolds and creates Voronoi diagrams based on charts.

提出采用黎曼流形描述研究对象和基于坐标卡生成Voronoi图的算法思路。

It also makes an introduction to Lie groups, the de Rham theorem, and Riemannian manifolds.

同时也对李群，de Rham定理，和黎曼流形作了简要介绍。

In 1996, Shen applied Hamilton's Ricci flow to study the metric deformation on Riemannian manifolds with boundary.

最近在[P1]，[P2]中，Perelman利用Ricci流的方法向Poincaré猜想的最后解决又迈进了一大步。

This course should help students master definitions, basic peoperties and methods of differentiable and Riemannian manifolds, increase their ability from parts to a whole.

通过本课程的学习，希望学生能初步掌握微分流形的基本概念、方法和技巧，学习从局部到整体的数学技巧。

According to the idea and theorem, this paper describes the algorithm of creating charts for two-dimensional Riemannian manifolds and presents the definitions of transition and blend functions.

按照算法思路和存在定理，详细描述了二维黎曼流形上创建坐标卡的算法，并给出流形上转换函数和混合函数的定义方法。

For the case of waveduide R~2×M, where M be Zoll manifolds, if the initial data is small enough, we can use the special distribution of eigenvalues of Laplace-Beltrami operator on Zoll manifold, the estimate of the energy and the technique of normal form to prove the existence of global solutions for nonlinear Klein-Gordon equations.

对波管R~2×M上的非线性Klein-Gordon方程，其中M为Zoll流形，如果初值足够小，利用Zoll流形上Laplace-Beltrami算子的特征值的分布，并结合能量估计和法形式技巧，我们证明了整体解的存在性。

Based on the theory about nonlinear normal modes and normal form, a method of normal mode invariant manifolds for the analysis of simple Hopf bifurcating solutions is presented.

基于非线性模态不变流形及范式理论，针对一类非线性结构振动系统和机电耦合系统，提出一种分析其简单Hopf分叉解的模态不变流形方法。

But we don't care about Battlegrounds.

但我们并不在乎沙场中的显露。

Ah! don't mention it, the butcher's shop is a horror.

啊！不用提了。提到肉，真是糟透了。