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
Famous quotes containing the words complex and/or manifold:
“Uneducated people are unfortunate in that they do grasp complex issues, educated people, on the other hand, often do not understand simplicity, which is a far greater misfortune.”
—Franz Grillparzer (1791–1872)
“A large city cannot be experientially known; its life is too manifold for any individual to be able to participate in it.”
—Aldous Huxley (1894–1963)