向量丛

This pepediscusses compact submanifoldsoftheunit sphere Study is made on conditions ofsubmanifolds with parallel mean curvature vector,submanifolds with flat normal bundle and pseudo-umbilical submanifolds to be umbilical respectively.

本文讨论球的紧致子流形，研究具平行平均曲率向量的，具平坦法丛的、以及伪脐子流形成为全脐子流形的条件，得到几个关于第二基本形式长度千方S的pinching条件。

In exterior differentiation, one studies tensors, exterior algebra, tangent bundle, tangent vector fields, one-parameter groups action on a manifold, Frobenius's theorem, tensors fields, exterior differential form, integration on manifolds, Stokes's theorem etc.

外微分部分主要涉及外代数、切丛，光滑切向量场，单参数变换群，光滑张量场，外微分形式，Frobenius定理，外微分形式的积分，Stokes定理及其应用等。

The stable vector bundle is constructed which is the mirror image of a special Lagrangian section with branched singularities of K3 surface or 2 dimentional complex torus.

用hyperKaehler rotation与反自对偶联络的技巧，给出了K-3曲面与复环面上2-重特殊拉格朗日截面所对应的稳定向量丛。

In chapter 2 we recall the basic facts about Riemannian manifold and some notions of the transform theory on Riemannian manifolds.

首先，利用给定流形的向量丛上联络的存在性给出流形上的不可积分布上非完整联络的存在性证明，进而证明了次黎曼联络的存在唯一性，并以此为出发点研究了次黎曼流形中仿射变换、等距变换、共形变换和射影变换下的一些不变性质，给出了相应变换下的一些不变量。

Newton's method; Riemannian manifold; Smale's point estimate theory; section of a vector bundle; geodesic; Lie group; one-parameter subgroup

基础科学，数学，几何、拓扑Newton法； Riemann流形； Smale点估计理论；向量丛的截面；测地线；李群；单参数子群

To do so, at first, we introduce the characteristic triple, the invariant subbundle and invariant vector field.

为此，首先引入了特征三元组的概念，并定义了不变子丛及不变向量场。

The main ingredient in the set-theoretical part of Kobayashi-Hitchin correspondence is the followingTheorem 01. A stable holomorphic vector bundle E admits a Hermitian-Einstein metric.

其中重要的一步是如下的定理1.M是一紧复流形，设E是M上一稳定的向量丛，则E上存在有Hermitian-Einstein度量。

Keywords: Calabi-Yau manifold; special Lagrangian fibration; stable vector bundle; special Lagrangian submanifold; mirror symmetry.

中文关键词：卡拉比-丘流形；特殊拉格朗日纤维化；稳定向量丛；特殊拉格朗日子流形；镜对称

If you are unfortunate enough to the lovelorn, please tell me, I will help you out, really, please contact me!

如果你不幸失恋了，请告诉我，我会帮助你摆脱困境，真的，请联系我啦！

China's plan to cut energy intensity by 20 percent and pollutant discharges by 10 percent between 2006 and 2010 is a case in point.

中国计划在2006年到2010间降低20%的能源强度和减少10%的主要污染物排放，就是一个这样的例子。