Almost complex manifold

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.

Related Topics:
Mathematics - Smooth manifold - Linear complex structure - Tangent space - Complex manifold - Symplectic geometry

~ ~ ~ ~ ~ ~ ~ ~ ~ ~