An almost complex structure on a smooth manifold 
is a smooth bundle endomorphism 
of its tangent bundle such that 
. It makes each tangent space into a complex
vector space, so an almost complex manifold has even real dimension. An almost
complex structure comes from a complex manifold
precisely when it is integrable. Every Kähler
manifold carries an almost complex structure compatible with both its Riemannian
metric and symplectic form.
Almost Complex Structure
See also
Complex Manifold, Complex Structure, Kähler Manifold, Tangent BundleExplore with Wolfram|Alpha
References
McDuff, D. and Salamon, D. Introduction to Symplectic Topology, 2nd ed. Oxford, England: Oxford University Press, 1998.Cite this as:
Weisstein, Eric W. "Almost Complex Structure." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/AlmostComplexStructure.html