On the Geometry of Tangent Bundles with the Rescaled Metric
  For a Riemannian manifold $M$, we determine some curvature properties of a tangent bundle equipped with the rescaled metric.The main aim of this paper is to give explicit formulae for the rescaled metric on $TM$, and investigate the geodesics on the tangent bundle with respect to the rescaled Sasaki metric. 
Jian Wang, Yong Wang
math.DG