Notes on the second-order tangent bundles with the deformed Sasaki metric

Abstract

The paper deals with the second-order tangent bundle $T^{2}M$ with the deformed Sasaki metric $\overline{g}$ over an n−dimensional Riemannian manifold $(M,g)$. We calculate all Riemannian curvature tensor fields of the deformed Sasaki metric $\overline{g}$ and search Einstein property of $T^{2}M$. Also the weakly symmetry properties of the deformed Sasaki metric are presented.

Keywords

• Second-order tangent bundle
• deformed Sasaki metric
• weakly symmetric
• curvature tensor field
• lifts

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