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
Famous quotes containing the words complex and/or manifold:
“All propaganda or popularization involves a putting of the complex into the simple, but such a move is instantly deconstructive. For if the complex can be put into the simple, then it cannot be as complex as it seemed in the first place; and if the simple can be an adequate medium of such complexity, then it cannot after all be as simple as all that.”
—Terry Eagleton (b. 1943)
“Before abstraction everything is one, but one like chaos; after abstraction everything is united again, but this union is a free binding of autonomous, self-determined beings. Out of a mob a society has developed, chaos has been transformed into a manifold world.”
—Novalis [Friedrich Von Hardenberg] (1772–1801)