On tangent bundles with Sasakian metrics of Finslerian and Riemannian manifolds

Abstract

On the basis of the so-called phase completion the notion of vertical, horizontal and complete objects is defined in the tangent bundles over Finslerian and Riemannian manifold. Such a tangent bundle is made into a manifold of almost Kaehlerian structure by endowing it with Sasakian metric. The components of curvature tensors with respect to the adapted frame are presented. This having been done it is shown possible to study the differential geometry of Finslerian spaces by dealing with that of their own tangent bundles.