In differential geometry, a complex manifold is a manifold with an atlas of charts to the open unit disk in Cn, such that the transition maps are holomorphic.
The term complex manifold is variously used to mean a complex manifold in the sense above (which can be specified as an integrable complex manifold), and an almost complex manifold.
Read more about Complex Manifold: Implications of Complex Structure, Examples of Complex Manifolds, Disk Vs. Space Vs. Polydisk, Almost Complex Structures, Kähler and Calabi–Yau Manifolds
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