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Holomorphic Vector Bundle


A complex vector bundle is a vector bundle pi:E->M whose fiber bundles pi^(-1)(m) are a copy of C^k. pi is a holomorphic vector bundle if it is a holomorphic map between complex manifolds and its transition functions are holomorphic. The simplest example is a holomorphic line bundle, where the fiber is simply a copy of C.


See also

Complex Manifold, Hermitian Metric, Holomorphic Function, Holomorphic Line Bundle, Holomorphic Tangent Bundle, Vector Bundle

This entry contributed by Todd Rowland

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Cite this as:

Rowland, Todd. "Holomorphic Vector Bundle." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/HolomorphicVectorBundle.html

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