Examples
For every integer n, the flat space admits an almost complex structure. An example for such an almost complex structure is : for odd i, for even i.
The only spheres which admit almost complex structures are S2 and S6. In the case of S2, the almost complex structure comes from an honest complex structure on the Riemann sphere. The 6-sphere, S6, when considered as the set of unit norm imaginary octonions, inherits an almost complex structure from the octonion multiplication.
Read more about this topic: Almost Complex Manifold
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