Some Problems Concerning with Sasaki Metric on the Second-Order Tangent Bundles

Year 2020, Volume: 13 Issue: 2, 75 - 86, 15.10.2020

Abdullah Mağden , Aydın Gezer , Kübra Karaca

https://doi.org/10.36890/iejg.750905

Cited By: 5

Abstract

In this paper, we consider a second-order tangent bundle equipped with
Sasaki metric over a Riemannian manifold. All forms of curvature tensor
fields are computed. We obtained the relation between the scalar curvature
of the base manifold and the scalar curvature of the second-order tangent
bundle and presented some geometric results concerning with kinds of
curvature tensor fields. Also, we search the weakly symmetry property of the
second-order tangent bundle. Finally, we end our paper with statistical
structures on the second-order tangent bundle.

Keywords

Curvature tensor field, lifts, econd-order tangent bundle, statistical structure, weakly symmetry

Supporting Institution

TUBİTAK

Project Number

AR-GE 3001 Project No. 118F190

Thanks

The paper is supported by the Scientific and Technological Research Council of Turkey, AR-GE 3001 Project No. 118F190

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