Differential Forms On A Complex Manifold
Suppose that M is a complex manifold. Then there is a local coordinate system consisting of n complex-valued functions z1,...,zn such that the coordinate transitions from one patch to another are holomorphic functions of these variables. The space of complex forms carries a rich structure, depending fundamentally on the fact that these transition functions are holomorphic, rather than just smooth.
Read more about this topic: Complex Differential Form
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