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Keywords:
Almost complex structure; curvature operator; integrability; tangent bundle
Almost complex structure; curvature operator; integrability; tangent bundle
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.
References:
[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 10.1093/qmath/hap040 | MR 2805204
[2] Aguilar, R. M.: Isotropic almost complex structures on tangent bundles. Manuscripta Math., 90, 4, 1996, 429-436, DOI 10.1007/BF02568316 | MR 1403714
[3] Biswas, I., Loftin, J., Stemmler, M.: Flat bundles on affine manifolds. Arabian Journal of Mathematics, 2, 2, 2013, 159-175, DOI 10.1007/s40065-012-0064-8 | MR 3055288
[4] Choi, J., Mullhaupt, A. P.: Kählerian information geometry for signal processing. Entropy, 17, 2015, 1581-1605, DOI 10.3390/e17041581 | MR 3344374
[5] Friswell, R. M., Wood, C. M.: Harmonic vector fields on pseudo-Riemannian manifolds. Journal of Geometry and Physics, 112, 2017, 45-58, DOI 10.1016/j.geomphys.2016.10.015 | MR 3588756
[6] Lisi, S.T.: Applications of Symplectic Geometry to Hamiltonian Mechanics. 2006, PhD thesis, New York University. MR 2708404
[7] Petersen, P.: Riemannian Geometry. 2006, Springer, MR 2243772 | Zbl 1220.53002
[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 10.4064/ap103-3-2 | MR 2876391
[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 3037240
[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 10.1007/s11401-011-0646-3 | MR 2805406
[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 3126092
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