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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 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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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     title = {A new class of almost complex structures on tangent bundle of a {Riemannian} manifold},
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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/

[1] Abbassi, M.T.K., Calvaruso, G., Perrone, D.: Harmonic sections of tangent bundles equipped with Riemannian g-natural metrics. Q. J. Math., 62, 2, 2011, 259-288, | DOI | MR

[2] Aguilar, R. M.: Isotropic almost complex structures on tangent bundles. Manuscripta Math., 90, 4, 1996, 429-436, | DOI | MR

[3] Biswas, I., Loftin, J., Stemmler, M.: Flat bundles on affine manifolds. Arabian Journal of Mathematics, 2, 2, 2013, 159-175, | DOI | MR

[4] Choi, J., Mullhaupt, A. P.: Kählerian information geometry for signal processing. Entropy, 17, 2015, 1581-1605, | DOI | MR

[5] Friswell, R. M., Wood, C. M.: Harmonic vector fields on pseudo-Riemannian manifolds. Journal of Geometry and Physics, 112, 2017, 45-58, | DOI | MR

[6] Lisi, S.T.: Applications of Symplectic Geometry to Hamiltonian Mechanics. 2006, PhD thesis, New York University. | MR

[7] Petersen, P.: Riemannian Geometry. 2006, Springer, | MR | Zbl

[8] Peyghan, E., Heydari, A., Far, L. Nourmohammadi: On the geometry of tangent bundles with a class of metrics. Annales Polonici Mathematici, 103, 2012, 229-246, | DOI | MR

[9] Peyghan, E., Nasrabadi, H., Tayebi, A.: The homogenous lift to the $(1,1)$-tensor bundle of a Riemannian metric. Int. J. Geom Meth. Modern Phys., 10, 4, 2013, 18p, | MR

[10] Salimov, A. A., Gezer, A.: On the geometry of the $(1,1)$-tensor bundle with Sasaki type metric. Chinese Ann. Math. Ser. B, 32, 3, 2011, 1-18, | DOI | MR

[11] Zhang, J., Li, F.: Symplectic and Kähler structures on statistical manifolds induced from divergence functions. Conference paper in Geometric Science of Information, 2013, 595-603, Springer, | MR