Some Problems Concerning with Sasaki Metric on the Second-Order Tangent Bundles
Int Electronic Journal Geometry
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.
Curvature tensor field, lifts, second-order tangent bundle, statistical structure, weakly symmetry
International Electronic Journal Of Geometry
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