有关Griffiths正的全纯向量丛的研究

典则度量的存在性是几何分析领域重要的研究问题。 对于向量丛，经典的Donaldson-Uhlenbeck-Yau定理告诉我们：稳定的向量丛上存在Hermitian-Einstein度量，那么Griffiths正稳定的向量丛上是否存在Griffiths正的Hermitian-Einstein度量呢？从这个问题出发，本项目主要研究：.1.Griffiths正沿Hermitian-Yang-Mills热流的性质.申请者希望借助于Hamilton、Mok、Ustinovskiy以及Wan关于正性保持的方法，来研究Griffiths正沿Hermitian-Yang-Mills热流是否保持。.2.Griffiths正稳定向量丛上的陈数.申请者希望得到Griffiths正稳定向量丛上更优的陈数不等式。以期从陈数不等式给出向量丛不同时满足Griffiths正和稳定的一个判断。

The existence of canonical metric is an important problem in geometric analysis. The classical Donaldson-Uhlenbeck-Yau theorem tells us that stable bundles admit Hermitian-Einstein metric. However, whether there exists Griffiths positive Hermitian-Einstein metric on Griffiths positive-stable holomorphic vector bundles? Starting from this question, we mainly want to study the followings:.1.The properties of Griffiths positivity along the Hermitian-Yang-Mills flow.We want to study whether the Griffiths positivity is preserved along the Hermitian-Yang-Mills flow with the help of predecessors, such as Hamilton for Ricci flow, Mok for Kahler Ricci flow, Ustinovskiy for Hermitian curvature flow and Wan for his work that the Griffiths positivity of vector bundle is equivalent to the pseudoconvexity of log Finsler metric of the vector bundle..2. Chern numbers of Griffiths positive -stable vector bundle.We want to obtain more stronger Chern number inequality of Griffith positive-stable vector bundle. Thus, we can give a judgment of a vector bundle not satisfying Griffiths positivity and stability at the same time.