Some Notes on Berger Type Deformed Sasaki Metric in the Cotangent Bundle

Year 2021, , 348 - 360, 29.10.2021

Abderrahım Zagane

https://doi.org/10.36890/iejg.911446

Cited By: 3

Abstract

In the present paper, we study some notes on Berger type deformed Sasaki metric in the cotangent bundle $T^{\ast }M$ over an anti-paraKähler manifold $(M,\phi ,g)$. We characterize some geodesic properties for this metric. Next we also construct some almost anti-paraHermitian structures on $T^{\ast }M$ and search conditions for these structures to be anti-paraKähler and quasi-anti-paraKähler with respect to the Berger type deformed Sasaki metric.

Keywords

Horizontal lift and vertical lift, cotangent bundle, Berger type deformed Sasaki metric, geodesic, paracomplex

Thanks

Dear Editor-in-Chief, Thank you for accepting submit article our manuscript " Some notes on Berger type deformed Sasaki metric in the cotangent bundle". We would be very happy, if our manuscript meets the Journal of Publishing standards "International Electronic Journal of Geometry". Thanks again, Author

References

• [1] Ağca, F.: g-Natural Metrics on the cotangent bundle. Int. Electron. J. Geom. 6(1), 129-146 (2013).
• [2] Ağca, F., Salimov, A. A.: Some notes concerning Cheeger-Gromoll metrics. Hacet. J. Math. Stat. 42(5), 533-549 (2013).
• [3] Altunbas, M., Simsek, R., Gezer A.: A Study Concerning Berger type deformed Sasaki Metric on the Tangent Bundle. Zh. Mat. Fiz. Anal. Geom. 15(4), 435-447 (2019). https://doi.org/10.15407/mag15.04.435
• [4] Cruceanu, V., Fortuny, P., Gadea, P. M.: A survey on paracomplex geometry. Rocky Mountain J. Math. 26(1), 83-115 (1996). doi:10.1216/rmjm/1181072105
• [5] De León, M., Rodrigues, P. R. Methods of Differential Geometry in Analytical Mechanics. North-Holland Mathematics Studies, (1989). https://doi.org/10.1002/zamm.19910710314
• [6] Ganchev, G. T., Borisov, A. V.: Note on the almost complex manifolds with a Norden metric. C. R. Acad. Bulgarie Sci. 39(5), 31-34 (1986).
• [7] Gezer, A., Altunbas, M.: On the Rescaled Riemannian Metric of Cheeger Gromoll Type on the Cotangent Bundle. Hacet. J. Math. Stat. 45(2), 355-365 (2016). https:// Doi:10.15672/HJMS.20164515849
• [8] Manev, M., Mekerov, D.: On Lie groups as quasi-Kähler manifolds with Killing Norden metric. Adv. Geom. 8(3), 343-352 (2008). https://doi.org/10.1515/ADVGEOM.2008.022
• [9] Ocak, F.: Notes About a New Metric on the Cotangent Bundle. Int. Electron. J. Geom. 12(2), 241-249 (2019). https://doi.org/10.36890/iejg.542783
• [10] Patterson, E. M., Walker, A. G.: Riemannian extensions. Quart. J.Math. Oxford Ser. 2(3), 19-28 (1952).
• [11] Salimov, A. A., Agca, F.: Some Properties of Sasakian Metrics in Cotangent Bundles. Mediterr. J. Math. 8(2), 243-255 (2011). https://doi.org/10.1007/s00009-010-0080-x
• [12] Salimov, A. A., Gezer, A., Iscan, M.: On anti-paraKähler structures on the tangent bundles. Ann. Polon. Math. 103(3), 247-261 (2012). https://doi.org/10.4064/ap103-3-3
• [13] Salimov, A. A., Iscan, M., Akbulut, K.: Notes on para-Norden-Walker 4-manifolds. Int. J. Geom. Methods Mod. Phys. 7(8), 1331-1347 (2010). https://doi.org/10.1142/S021988781000483X
• [14] Salimov, A. A., Iscan, M., Etayo, F.: Para-holomorphic B-manifold and its properties. Topology Appl. 154(4), 925-933 (2007). https://doi.org/10.1016/j.topol.2006.10.003
• [15] Sekizawa, M.: Natural transformations of affine connections on manifolds to metrics on cotangent bundles. In: Proceedings of 14thWinter School on Abstract Analysis (Srni, 1986), Rend. Circ. Mat. Palermo 14, 129-142 (1987).
• [16] Yano, K., Ako, M.: On certain operators associated with tensor field. Kodai Math. Sem. Rep. 20(4), 414-436 (1968). https://doi.org/10.2996/kmj/1138845745
• [17] Yano, K., Ishihara, S.: Tangent and Cotangent Bundles, M. Dekker, New York, (1973).
• [18] Zagane, A.: A new class of metrics on the cotangent bundle. Bull. Transilv. Univ. Brasov Ser. III 13(62)(1), 285-302 (2020). https://doi.org/10.31926/but.mif.2020.13.62.1.22
• [19] Zagane, A.: Berger type deformed Sasaki metric and harmonicity on the cotangent bundle. Int. Electron. J. Geom 14(1), 183-195 (2021). https://doi.org/10.36890/IEJG.793530