Complex Vector Bundle

A complex vector bundle is a vector bundle pi:E->M whose fiber bundle pi^(-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 pi is holomorphic, then it is called a holomorphic vector bundle.

See also

Bundle, Complex Vector Space, Holomorphic Vector Bundle, Manifold, Vector Space

This entry contributed by Todd Rowland

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Cite this as:

Rowland, Todd. "Complex Vector Bundle." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein.

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