Authors: Amir Baghban ; Esmaeil Abedi

In this paper, the standard almost complex structure on the tangent bunle of a Riemannian manifold will be generalized. We will generalize the standard one to the new ones such that the induced (0, 2)-tensor on the tangent bundle using these structures and Liouville 1-form will be a Riemannian metric. Moreover, under the integrability condition, the curvature operator of the base manifold will be classified.

• 32Q60 - Almost complex manifolds
• 58A30 - Vector distributions (subbundles of the tangent bundles)