The holomorphic tangent bundle to a complex manifold is given by its complexified tangent vectors which are of type 
. In a coordinate chart 
,
the bundle is spanned by the local bundle sections 
.
The antiholomorphic sections are spanned by 
, of type 
, where 
denotes the complex conjugate.
Holomorphic Tangent Bundle
See also
Complex Structure, CR-Structure, Hermitian Metric, Holomorphic Line Bundle, Holomorphic Vector Bundle, Tangent BundleThis entry contributed by Todd Rowland
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Cite this as:
Rowland, Todd. "Holomorphic Tangent Bundle." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/HolomorphicTangentBundle.html