Acknowledgement
This note was supported by National Algerian PRFU project.
References
- F. Agca, g-natural metrics on the cotangent bundle, Int. Electron. J. Geom. 6 (2013), no. 1, 129-146.
- F. Agca and A. A. Salimov, Some notes concerning Cheeger-Gromoll metrics, Hacet. J. Math. Stat. 42 (2013), no. 5, 533-549.
- M. Altunbas, R. Simsek, and A. Gezer, A study concerning Berger type deformed Sasaki metric on the tangent bundle, Zh. Mat. Fiz. Anal. Geom. 15 (2019), no. 4, 435-447. https://doi.org/10.15407/mag15.04.435
- A. Gezer and M. Altunbas, On the rescaled Riemannian metric of Cheeger-Gromoll type on the cotangent bundle, Hacet. J. Math. Stat. 45 (2016), no. 2, 355-365.
- F. Ocak, Notes about a new metric on the cotangent bundle, Int. Electron. J. Geom. 12 (2019), no. 2, 241-249. https://doi.org/10.36890/iejg.542783
- F. Ocak and S. Kazimova, On a new metric in the cotangent bundle, Trans. Natl. Acad. Sci. Azerb. Ser. Phys.-Tech. Math. Sci. 38 (2018), no. 1, Mathematics, 128-138.
- E. M. Patterson and A. G. Walker, Riemann extensions, Quart. J. Math. Oxford Ser. (2) 3 (1952), 19-28. https://doi.org/10.1093/qmath/3.1.19
- A. A. Salimov and F. Agca, Some properties of Sasakian metrics in cotangent bundles, Mediterr. J. Math. 8 (2011), no. 2, 243-255. https://doi.org/10.1007/s00009-010-0080-x
- A. A. Salimov, M. Iscan, and F. Etayo, Paraholomorphic B-manifold and its properties, Topology Appl. 154 (2007), no. 4, 925-933. https://doi.org/10.1016/j.topol.2006.10.003
- S. Sasaki, On the differential geometry of tangent bundles of Riemannian manifolds. II, Tohoku Math. J. (2) 14 (1962), 146-155. https://doi.org/10.2748/tmj/1178244169
- M. Sekizawa, Natural transformations of affine connections on manifolds to metrics on cotangent bundles, Rend. Circ. Mat. Palermo (2) Suppl. No. 14 (1987), 129-142.
- K. Yano and S. Ishihara, Tangent and Ctangent Bundles: differential geometry, Marcel Dekker, Inc., New York, 1973.