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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.

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