  We show in this article that if a holomorphic vector bundle has a nonnegative
Hermitian metric in the sense of Bott and Chern, which always exists on
globally generated holomorphic vector bundles, then some special linear
combinations of Chern forms are strongly nonnegative. This particularly implies
that all the Chern numbers of such a holomorphic vector bundle are nonnegative
and can be bounded below and above respectively by two special Chern numbers.
As applications, we obtain a family of new results on compact connected complex
manifolds which are homogeneous or can be holomorphically immersed into complex
tori, some of which improve several classical results.
