Complex manifold

In <a href="/facts/Differential_geometry/c04XmyLu">differential geometry</a> and <a href="/facts/Complex_geometry/ekCsxAXb">complex geometry</a>, a complex manifold is a <a href="/facts/Manifold/rXPERJtu">manifold</a> with a complex structure, that is an <a href="/facts/Atlas_(topology)/pjoya29t">atlas</a> of <a href="/facts/Chart_(topology)/pjoya29t">charts</a> to the <a href="/facts/Open_unit_disc/phrUu7yC">open unit disc</a> in the <a href="/facts/Complex_coordinate_space/4zCD19qb">complex coordinate space</a> 
 
 
 
 
 
 C
 
 
 n
 
 
 
 
 {\displaystyle \mathbb {C} ^{n}}
 
, such that the <a href="/facts/Transition_map/pjoya29t">transition maps</a> are <a href="/facts/Holomorphic_function/kVzthtEf">holomorphic</a>.
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 <a href="/facts/Almost_complex_manifold/wsXTsuC6">almost complex manifold</a>.

Complex manifold open-in-new

Complex manifold