Holomorphic Vector Bundle on Hopf Manifolds with Abelian Fundamental Groups

Let X be a Hopf manifolds with an Abelian fundamental group.E is a holomorphic vector bundle of rank r with trivial pull-back to W=■~n-{0}.We prove the existence of a non-vanishing section of L■E for some line bundle on X and study the vector bundles filtration structure of E. These generalize the results of D.Mall about structure theorem of such a vector bundle E.