F-geodesics on the second order tangent bundle over a Riemannian manifold

Abstract

Let (M,g) be a Riemannian manifold and T²M be its second order tangent bundle. In this paper, we deal with certain characterizations of F-geodesics (which generalize both classical geodesics and magnetic curves) on the second order tangent bundle T²M and the hypersurface T_{1,1}²M with respect to some natural metrics.