Complex manifold

In differential geometry and complex geometry, a complex manifold or a complex analytic manifold is a manifold with a complex structure, that is an atlas of charts to the open unit ball in the complex coordinate space${\displaystyle \mathbb {C} ^{n}}$, 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) or an almost complex manifold.