On the geodesics of deformed Sasaki metric

Authors: NOUR ELHOUDA DJAA, ABDERRAHIM ZAGANE

Abstract: We define in this note a natural metric over the tangent bundle $TM$ by using a vertical deformation of Sasaki metric. First we present the geometric result concerning the Levi-Civita connection and all forms of Riemannian curvature tensors of this metric. Secondly, we study the geodesics on the tangent bundle $TM$ and unit tangent bundle $T_{1}M$. Finally, we characterize the geodesic curvatures on $T_{1}M$.

Keywords: Deformed Sasaki metric, geodesics, tangent bundle, unit tangent bundle

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