A complex vector bundle is a vector bundle 
whose fiber bundles 
are a copy of 
. 
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 
.
Holomorphic Vector Bundle
See also
Complex Manifold, Hermitian Metric, Holomorphic Function, Holomorphic Line Bundle, Holomorphic Tangent Bundle, Vector BundleThis entry contributed by Todd Rowland
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Cite this as:
Weisstein, Eric W., with contributions by Todd Rowland. "Holomorphic Vector Bundle." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/HolomorphicVectorBundle.html