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

Abstract

In this paper, we consider a second-order tangent bundle equipped with Sasaki metric over aRiemannian manifold. All forms of curvature tensor fields are computed. We obtained the relationbetween the scalar curvature of the base manifold and the scalar curvature of the second-ordertangent bundle and presented some geometric results concerning with kinds of curvature tensorfields. 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.