Geodesic
A new class of almost complex structures on tangent bundle of a Riemannian manifold
Communications in Mathematics, Tome 26 (2018) no. 2, pp. 137-145

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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.
Classification : 32Q60, 58A30
Keywords: Almost complex structure; curvature operator; integrability; tangent bundle 
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     author = {Baghban, Amir and Abedi, Esmaeil},
     title = {A new class of almost complex structures on tangent bundle of a {Riemannian} manifold},
     journal = {Communications in Mathematics},
     pages = {137--145},
     publisher = {mathdoc},
     volume = {26},
     number = {2},
     year = {2018},
     mrnumber = {3898198},
     zbl = {07058960},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/COMIM_2018__26_2_a4/}
}
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Baghban, Amir; Abedi, Esmaeil. A new class of almost complex structures on tangent bundle of a Riemannian manifold. Communications in Mathematics, Tome 26 (2018) no. 2, pp. 137-145. http://geodesic.mathdoc.fr/item/COMIM_2018__26_2_a4/