Usually means: Atlas of charts with holomorphic transitions.
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We found 4 dictionaries that define the word complex manifold:

General (1 matching dictionary)
  1. Complex Manifold, Complex manifold: Wikipedia, the Free Encyclopedia

Science (3 matching dictionaries)
  1. Complex Manifold: Eric Weisstein's World of Mathematics
  2. complex manifold, Complex manifold: PlanetMath Encyclopedia

Definitions from Wikipedia (Complex manifold)

noun:  In differential geometry and complex geometry, a complex manifold is a manifold with a complex structure, that is an atlas of charts to the open unit discOne must use the open unit disc in the as the model space instead of because these are not isomorphic, unlike for real manifolds.

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