Journal of Mathematical Physics, Analysis, Geometry
2019, vol. 15, No 4, pp. 435-447   https://doi.org/10.15407/mag15.04.435     ( to contents , go back )
https://doi.org/10.15407/mag15.04.435

Study Concerning Berger Type Deformed Sasaki Metric on the Tangent Bundle

Murat Altunbas

Erzincan Binali Yıldırım University, Department of Mathematics, Erzincan, Turkey
E-mail: maltunbas@erzincan.edu.tr

Ramazan Simsek

Bayburt University, Technical Sciences Vocational School, Bayburt, Turkey
E-mail: rsimsek@bayburt.edu.tr

Aydın Gezer

Ataturk University, Department of Mathematics, Erzurum, 25240, Turkey
E-mail: aydingzr@gmail.com

Received September 17, 2018, revised December 10, 2018.

Abstract

Let TM be the tangent bundle over an almost anti-paraHermitian manifold endowed with Berger type deformed Sasaki metric gBS. In this paper,first, we obtain the Levi-Civita connection of this metric and study geodesics on TM. Secondly, we construct some almost anti-paraHermitian structures on TM and search conditions for these structures to be anti-paraKähler and quasi-anti-paraKähler. Finally, we present certain Riemannian curvature properties of (TM, gBS).

Mathematics Subject Classification 2000: 53C07, 53C55, 53C22.
Key words: Berger type deformed Sasaki metric, paracomplex structure, geodesics, tangent bundle.

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