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A new class of almost complex structures on tangent bundle of a Riemannian manifold. (English) Zbl 1419.32005
Summary: 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.

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