向量丛

一类希尔伯特级数的计算以及Frobenius态射下向量丛的稳定性

A Computation of Some Hilbert Series and the Stability of a Vector Bundle under Frobenius Morphism

我们设M是一紧复流形，E为其上的可微分向量丛。

Let M be a compact complex manifold , E a differentiable complex vector bundle over M , and g resp .

有关这方面问题的研究称为向量丛的Brill-Noether理论。

The study of these problems is called Brill-Noether theory for vector bundles .

论文第四部分给出本文的主要结果，即联系于实向量丛一对截面的一个Poincaré–Hopf型公式及其证明。

In the last chapter is the mainly research result in this thesis , which gives the proof about a Poincar é - Hopf type formula for a pair of sections of a real vector bundle .

在本文中，我们给出并证明了由截面生成的二维向量丛的消没定理、Clifford定理和存在定理，并部分地给出了这类二维向量丛的分类。

In this dissertation , we give and prove the vanishing theorem , the Clifford theorems and the existence theorem for rank two vector bundles generated by their sections , and partially give the classification of these vector bundles .

证明了完备、定向曲面的基本群在SU（2）中的表示空间可等同于该曲面上秩为2且具有平凡行列式丛的全纯向量丛的模空间.并且它们具有射影结构。

The representation space of the fundamental group of a closed , oriented Riemannian surface is identified with the moduli space of the holomorphic bundles of rank 2 with trivial determinant bundles over the surface and these spaces are proved to carry a projective structure .

把由向量丛态射诱导出的三个特殊丛推广到模丛态射中，得到了相应的三个模丛：ker丛、im丛和coker丛；

Expand three especial induced vector bundles induced by a morphism of vector bundles to those induced by a morphism of module bundles so that three module bundles , ker bundles , im bundles and coker bundles are obtained .

我们的方法和结论可以为更高维向量丛的Brill-Noether理论的研究奠定一定的基础。

Our methods and conclusions may lay some foundation for the study of the Brill-Noether theory for vector bundles of higher dimensions .

我们的目的就是在经典的线丛Brill-Noether理论的基础上，讨论二维向量丛的Brill-Noether理论。

Our purpose is the discussion about the Brill-Noether theory for rank two vector bundles on the basis of the classical theory for line bundles .

本文得到一些有关一类第一Betti数为奇数的曲面上的全纯向量丛的结果，以及例外Hopf曲面上的集合IS2（X，0）的描述。

In the present paper , we obtain some remarks on holomorphic vector bundles on some non-algebraic compact complex surfaces with odd first Betti number . In particular , we get a description of IS2 ( X , 0 ) of exceptional Hopf surface here .

消没定理中最低次数的寻找、Clifford定理中最小上界的确定、存在定理的条件、由截面生成的不可分解特殊二维向量丛分类的依据，这些是问题的主要难点。

The main difficulties in the discussion are finding the least degree in the vanishing theorem , determining the least upper bound in the Clifford theorems , the condition of the existence theorem and the criterion of classifying the indecomposable special rank two vector bundles generated by their sections .

近年来Douglas，Misra等人希望用复几何的方法来研究Hilbert模的几何不变量，例如一类Hilbert模对应的Hermitian全纯向量丛的曲率不变量。

In recent years , Douglas and Misra and other mathematicians want to study the geometric invariants of Hilbert module by using methods of complex geometry , for example , to study the curva-ture invariant of the Hermitian holomorphic vector bundles related to some classes of Hilbert modules .

本文对于联系于定向实向量丛的一对截面建立了一个Poincaré-Hopf型公式，推广了文献[1]中的一个相应结果。本文分四个部分。

In this thesis we will establish a Poincar é - Hopf type formula for a pair of sections of an oriented real vector bundle , which generalized a recent result of Feng-Li-Zhang in [ 1 ] . This thesis is divided into four chapters .

将线汇转化成向量丛后从理论上证明了这种转化的正确性，利用向量丛的截面理论证明了Backlund定理并给出一种固定边界而求面积最小的曲面的迭代条件。

After congruence of lines changes into vector bundles , its correctness is proved , and theorem of Backlund is proved by using sections of bundles . A condition of iteration is given for seeking minimal area of a curved surface with fixed boundary curve .

复向量丛上特殊度量和联络的存在性问题

On Existences of Special Metrics and Connections in Complex Vector Bundle

二维向量丛的最大子线丛

Some Remarks on Maximal Line Subbundles of Rank Two Vector Bundles

向量丛动力系统研究注记（Ⅰ）

Notes on a Study of Vector Bundle Dynamical Systems (ⅰ)

亏格二纤维曲面上的稳定向量丛的存在性

Existence of Stable Vector Bundles over Genus 2 Fiberized Surfaces

例外序列的概念来源于对于向量丛的研究。

The notation of exceptional sequence came from the study of vector bundles .

向量丛上的联络映射

The connection map of a vector manifold

由于对可分解的向量丛，问题可以转化为对相关线丛的讨论，因此我们主要讨论的是不可分解的情形，并进一步归结为对由截面生成的不可分解特殊二维向量丛的讨论。

Since the discussion for the decomposable vector bundles can be transferred to the line bundles involved , we primarily deal with the indecomposable ones , and further reduce to discuss the indecomposable special rank two vector bundles generated by their sections .

如何从纤维丛的底空间和纤维型的黎曼度量构造丛空间的黎曼度量，接着，定理1和定理2分别给出了向量丛和主丛关于这种度量的线素。

A new definition concerning the Riemannian metric of bundle spaces is given by using of the Riemannian metric of related base spaces and fibers . Theorem 1 and theorem 2 give the line elements of the metric for the vector bundles and for the principal bundles , respectively .