一类 Hopf 流形上的强可滤丛

Hopf流形是一类简单但却很重要的非代数流形,其上的全纯向量丛的性质是复几何研究的一个热点.研究了一类Hopf流形上强可滤丛的性质,得到了其上同调群的计算公式,证明了其第i(i>1)个陈类都为0,最后证明了一类具有交换基本群的Hopf曲面上的强可滤丛都为单丛.这些结果可应用于Hopf流形上连续向量丛的全纯结构存在性问题的研究.

Strongly Filtrable Bundles on a Type of Hopf Manifolds

Hopf manifolds is a simple but important class of compact non-algebraic manifolds.The properties of holomorphic vector bundles on them is received increase attention.In this paper,author consider the properties of strongly filtrable vector bundles on general Hopf manifolds.A computational formulas of the dimension of the cohomology group is obtained .And authors proved the i-th Chern class of strongly filtrable vector bundles on general Hopf manifolds is zero.Finally ,authors prove that strongly filtrable vector bundles on Hopf surface with Abelian Fundamental Groups are simple.These results can be applied to the research of existence problems of holomorphic structure on continuous vector bundles on hopf manifolds.