A complex vector bundle is a vector bundle whose fiber bundle is a complex vector space. It is not necessarily a complex manifold, even if its base manifold is a complex manifold. If a complex vector bundle also has the structure of a complex manifold, and is holomorphic, then it is called a holomorphic vector bundle.

# Complex 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. https://mathworld.wolfram.com/ComplexVectorBundle.html