查询词典 gauss curvature

In this paper,focusing on the symplectic manifolds,we discuss the Seiberg-Witteninvariants,some basic construction.the existence of symplectic forms,and the existenceof Riemannian metric of positive scalar curvature.

本文主要围绕辛流形，讨论其Seiberg-WItten不变量、辛流形的一些基本构造，辛形式的存在怀及其上是否存在具有正数量曲率的黎曼度量等问题而展开的。

Its main goal is to explore information relating to the large-scale geometrical structure of proper metric spaces, including noncompact complete Riemannian manifolds, finitely generated groups, etc., so as to establish connections among geometry, topology and analysis of the geometric spaces, and furthermore, to solve other important problems such as the Novikov conjecture, the Baum-Connes conjucture, the Gromov-Lawson-Rosenberg conjecture on positive scalar curvature and so on.

其主要目标是通过几何空间（如非紧完备黎曼流形、有限生成群等）大尺度几何结构的信息，建立几何空间的几何、拓扑与分析之间的联系，并应用于解决其他重要问题，如Novikov猜测、Baum-Connes猜测， Gromov-Lawson-Rosenberg正标量曲率猜测等。

The space-like hypersurfaces with constant scalar curvature in a de Sitter space were studied and a pinching theorem on the square of the norm of the second fundamental form was obtained.

研究de Sitter空间中具有常数量曲率的类空超曲面，将Cheng-Yau的自共轨运算元口作用在对称张量T上，得到了这类超曲面关於第二基本形式模长平方的一个拼挤定理，加强了已有的相应结果。

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 this article,we mainly study the space-like submanifolds with parallel mean curva-ture vector,constant scalar curvature or constant square length of the second fundamental form,respectively.We obtain some pinching theorems and rigidity results by estimating Laplace of the square length of the second fundamental form of the such submanifolds and using yaus maximum principle or Stokes Theorem.

本论文主要研究de Sitter空间中具有平行平均曲率向量、常数量曲率或第二基本形式模长平方是常数的三类类空子流形，并通过分别估计三种情形下子流形的第二基本形式模长平方的Laplace，利用Yau的极大值原理和Stokes定理，获得了这些子流形的一些拼挤定理和刚性定理。

If theharmonic index is finite,then each end may be represented by a non-constant positiveharmonic function,and these functions compose a partition of unity.For minimalhypersurfaces with finite total scalar curvature,we can explicitly estimate the harmonicindex.Moreover,the space of bounded harmonic functions are exactly generated bythose functions associated to each end.This gives geometric interpretations of the ends.

若调和指标有限，则每个端均可由一非常值的调和函数代表，它们形成了一个单位分解，对于全纯量曲率有限的极小超曲面，我们明确地估计了调和指标，进一步，有界调和函数正好由代表端的那些调和函数所生成，这就给出了端的几何解释。

Its main goal is to explore information in the K-theory groups of the index C*-algebras, the Roe algebras C*, by using the large-scale geometrical structure of proper metric spaces, including noncompact complete Riemannian manifolds, finitely generated groups, etc., so as to establish connections among geometry, topology and analysis of the geometric spaces, and furthermore, to solve other relating problems, say, the Novikov conjecture, the Gromov-Lawson-Rosenberg conjecture on positive scalar curvature, the idempotent problem in the theory of C*-algebras.

粗几何上的指标理论是"非交换几何"领域九十年代以来发展起来的重要研究方向，它孕育于非紧流形上的指标理论，其主要目标是通过几何空间（如非紧完备黎曼流形、有限生成群等）的大尺度几何结构探索指标代数，即 Roe代数，的K-理论群的信息，从而建立几何空间的几何、拓扑与分析之间的联系，并应用于解决其他重要问题，如Novikov猜测、Gromov-Lawson-Rosenberg正标量曲率猜测、群C*-代数幂等元问题等。

Elevation of IOP changes the curvature of the sclera but not that of the cornea.

IOP的升高改变了巩膜的曲率而不改变角膜的。

The scoliosis, however, is a small curvature and does not cause back pain.

scoliosis，然而，是一个小的屈曲并且不引起背痛。

Let x be an immersion of a compact Willmore surface M into the n-dimensional unit sphere Sn. In this thesis we first consider the Willmore surfaces in the unit 3-sphere, and establish an integral inequality for the square of the length of the trace free part of the second fundamental form and the mean curvature.

令x是一个从紧致威尔摩曲面M到n 维单位球面Sn的浸入，在本论文中我们首先考虑3维单位球面中的威尔摩曲面并建立一个包含第二基本型式迹为零部份的张量长度平方与平均曲率之积分不等式。

The witness also told the jury at the Royal Courts of Justice in London that he saw a paparazzo fighting with a member of the public who was trying to stop him taking pictures in the minutes before the emergency services arrived.

他还告诉在伦敦皇家法庭的陪审团，在急救服务到来之前，他当时看见一个狗仔队正和一群阻止他拍照的人打架。

The entire N／C program on a tape is made up of an accumulation of these successive data blocks.

纸带上的整个数控程序由这些连续数据单元连接而成。