On The Geometry Of Tangent Bundles With The Rescaled Metric

For a Riemannian manifold M, we determine some curvature properties of a tangentbundle equipped with the rescaled metric. The main aim of this paper is to give its Levi-Civita connection, its Riemann curvature tensor associated to the rescaled Sasaki metricand the rescaled Cheeger-Gromoll metric, and investigate the geodesics on the tangentbundle with respect to the rescaled Sasaki metric.