In mathematics, an almost complex manifold is a smooth manifold equipped with smooth linear complex structure on each tangent space. The existence of this structure is a necessary, but not sufficient, condition for a manifold to be a complex manifold. That is, every complex manifold is an almost complex manifold, but not vice-versa. Almost complex structures have important applications in symplectic geometry.
The concept is due to Ehresmann and Hopf in the 1940s.
Read more about Almost Complex Manifold: Formal Definition, Examples, Differential Topology of Almost Complex Manifolds, Integrable Almost Complex Structures, Compatible Triples, Generalized Almost Complex Structure
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