[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/CKMS.c200231

BERGER TYPE DEFORMED SASAKI METRIC ON THE COTANGENT BUNDLE

Zagane, Abderrahim (Department of Mathematics University Center of Relizane)

Publication Information

Communications of the Korean Mathematical Society / v.36, no.3, 2021 , pp. 575-592 More about this Journal

Abstract

In this paper, we introduce the Berger type deformed Sasaki metric on the cotangent bundle T^*M over an anti-paraKähler manifold (M, 𝜑, g) as a new natural metric with respect to g non-rigid on T^*M. Firstly, we investigate the Levi-Civita connection of this metric. Secondly, we study the curvature tensor and also we characterize the scalar curvature.

Keywords

Horizontal lift; vertical lift; cotangent bundles; Berger type deformed Sasaki metric; curvature tensor;

Citations & Related Records

Reference

1	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.
2	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 DOI
3	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 DOI
4	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.
5	K. Yano and S. Ishihara, Tangent and Ctangent Bundles: differential geometry, Marcel Dekker, Inc., New York, 1973.
6	F. Agca and A. A. Salimov, Some notes concerning Cheeger-Gromoll metrics, Hacet. J. Math. Stat. 42 (2013), no. 5, 533-549.
7	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 DOI
8	F. Ocak, Notes about a new metric on the cotangent bundle, Int. Electron. J. Geom. 12 (2019), no. 2, 241-249. DOI
9	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.
10	F. Agca, g-natural metrics on the cotangent bundle, Int. Electron. J. Geom. 6 (2013), no. 1, 129-146.
11	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 DOI
12	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 DOI