A complex vector bundle is a vector bundle π:E->M whose fiber bundle π^(-1)(x) is a complex vector space. It is not necessarily a complex manifold, even if its base manifold M is a complex manifold. If a complex vector bundle also has the structure of a complex manifold, and π is holomorphic, then it is called a holomorphic vector bundle.

bundle | complex vector space | holomorphic vector bundle | manifold | vector space