A remark on almost complex manifold with linear connections

The complex and almost complex manifolds are enormous and very fruitful fields for differential geometry. J.A. Schouten and D. Van Dantzig were the first to try to apply the finding in differential geometry of spaces with Riemannian metric and affine connection to the situation of complex structure spaces. C. Ehresmann defined an almost complex space as an even-dimensional differentiable manifold containing a tensor field with a square root of minus unity. The present paper intended to study, some fundamental properties with linear connections of an almost complex manifold. If almost complex structure be converted from a complex structure, then the various integrable and completely integrable condition has been investigated. Furthermore, the symmetric affine connections of almost complex manifold have also been investigated.