A Study of Para-K\"{a}hler-Norden Structures on Cotangent Bundle with The New Class of Metrics

Year 2021, Volume: 13 Issue: 2, 338 - 347, 31.12.2021

Abderrahım Zagane , Zagane Mohammed

Abstract

The main purpose of the present paper is to study almost para-complex-Norden properties concerning new class of metrics on the cotangent bundle.

Keywords

Cotangent bundles, horizontal lift and vertical lift, new class of metrics, almost para-complex structure, pure metric

Thanks

Thank you for accepting submit article our manuscript " A study of para-K\"{a}hler-Norden structures on cotangent bundle with the new class of metrics". We would be very happy, if our manuscript meets the " Turkish Journal of Mathematics and Computer Science". Thanks again, Corresponding author

References

• [1] Ağca, F., g-Natural metrics on the cotangent bundle, Int. Electron. J. Geom., 6(1)(2013), 129–146.
• [2] Ağca, F., Salimov, A.A., Some notes concerning Cheeger-Gromoll metrics, Hacet. J. Math. Stat., 42(5)(2013), 533–549.
• [3] Cruceanu, V., Une classe de structures g´eom´etriques sur le fibre cotangent, Tensor (N.S.), 53(1993), 196–201.
• [4] Cruceanu, V., Fortuny P., Gadea, P.M., A survey on paracomplex geometry, Rocky Mountain J. Math., 26(1996), 83–115.
• [5] De Leon, M., Rodrigues P.R., Methods of Dierential Geometry in Analytical Mechanics, North-Holland Mathematics Studies, 1989.
• [6] Ganchev, G.T., Borisov, A.V., Note on the almost complex manifolds with a Norden metric, C. R. Acad. Bulgarie Sci., 39(5)(1986) 31–34.
• [7] Gezer, A., On the tangent bundle with deformed Sasaki metric, Int. Electron. J. Geom., 6(2)(2013), 19–31.
• [8] Gezer, A., Altunbas, M., Notes on the rescaled Sasaki type metric on the cotangent bundle, Acta Math. Sci. Ser. B (Engl. Ed.) 34(1)(2014), 162–174.
• [9] Gezer, A., Altunbas, M., On the geometry of the rescaled Riemannian metric on tensor bundles of arbitrary type, Kodai Math. J. 38(1)(2015), 37–64.
• [10] Gezer, A. Altunbas, M., On the rescaled Riemannian metric of Cheeger Gromoll type on the cotangent bundle, Hacet. J. Math. Stat., 45(2)(2016), 355–365.
• [11] Manev, M., Mekerov, D., On Lie groups as quasi-K¨ahler manifolds with killing Norden metric, Adv. Geom., 8(3)(2008),343–352.
• [12] Ocak, F., Kazimova, S., On a new metric in the cotangent bundle, Trans. Natl. Acad. Sci. Azerb. Ser. Phys.-Tech. Math. Sci., 38(1)(2018), 128–138.
• [13] Patterson, E.M., Walker, A.G., Riemannian extensions, Quart. J.Math. Oxford Ser. 2(3)(1952), 19–28.
• [14] Salimov, A.A., Ağca, F., Some properties of Sasakian metrics in cotangent bundles, Mediterr. J. Math., 8(2)(2011), 243–255.
• [15] Salimov, A.A., Gezer, A., Iscan, M.,On para-Kahler-Norden structures on the tangent bundles, Ann. Polon. Math., 103(3)(2012), 247–261.
• [16] Salimov, A.A., Iscan, M., Akbulut, K., Notes on para-Norden-Walker 4-manifolds, Int. J. Geom. Methods Mod. Phys., 7(8)(2010), 1331–1347.
• [17] Salimov, A.A., Iscan, M., Etayo F., Para-holomorphic B-manifold and its properties, Topology Appl., 154(4)(2007), 925–933.
• [18] Sasaki, S., On the differential geometry of tangent bundles of Riemannian manifolds II, Tohoku Math. J. 14(1962), 146–155.
• [19] Sekizawa, M., Natural transformations of affine connections on manifolds to metrics on cotangent bundles, In: Proceedings of 14th Winter School on Abstract Analysis (Srni, 1986), Rend. Circ. Mat. Palermo 14(1987) 129–142.
• [20] Wang, J., Wang, Y., On the geometry of tangent bundles with the rescaled metric, arXiv:1104.5584v1.
• [21] Yano, K., Ako, M., On certain operators associated with tensor field, Kodai Math. Sem. Rep., 20(1968), 414–436.
• [22] Yano, K., Ishihara, S., Tangent and Cotangent Bundle, Marcel Dekker Inc., New York, 1973.
• [23] Zagane, A., A new class of metrics on the cotangent bundle, Bull. Transilv. Univ. Brasov Ser. III, 13(62)(1)(2020), 285–302.
• [24] Zayatuev, B.V., On Some Classes of Almost-Hermitian Structures on the Tangent Bundle, Webs and Quasigroups. T.S.U., 2002.