Some Problems Concerning with Sasaki Metric on the Second-Order Tangent Bundles - Mağden, Abdullah; Gezer, Aydin; Karaca, Kubra (Int Electronic Journal Geometry, 2020)
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; second-order tangent bundle; statistical structure; weakly symmetry