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A new class of almost complex structures on tangent bundle of a Riemannian manifold

Amir BaghbanEsmaeil Abedi — 2018

Communications in Mathematics

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.

Isotropic almost complex structures and harmonic unit vector fields

Amir BaghbanEsmaeil Abedi — 2018

Archivum Mathematicum

Isotropic almost complex structures J δ , σ define a class of Riemannian metrics g δ , σ on tangent bundles of Riemannian manifolds which are a generalization of the Sasaki metric. In this paper, some results will be obtained on the integrability of these almost complex structures and the notion of a harmonic unit vector field will be introduced with respect to the metrics g δ , 0 . Furthermore, the necessary and sufficient conditions for a unit vector field to be a harmonic unit vector field will be obtained.

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