Editing Complex manifold (section)

{{Short description|Manifold}}
{{No footnotes|date=October 2012}}
[[File:Holomorphic Maps.webm|thumb|right|Holomorphic Maps]]

In [[differential geometry]] and [[complex geometry]], a '''complex manifold''' is a [[manifold]] with a ''complex structure'', that is an [[atlas (topology)|atlas]] of [[chart (topology)|charts]] to the [[open unit disc]]<ref>One must use the open unit disc in the <math>\mathbb{C}^n</math> as the model space instead of <math>\mathbb{C}^n</math> because these are not isomorphic, unlike for real manifolds.</ref> in the [[complex coordinate space]] <math>\mathbb{C}^n</math>, such that the [[transition map]]s are [[Holomorphic function|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|''almost'' complex manifold]].