Magnetic trajectories on tangent sphere bundle with g-natural metrics

Abstract

We study magnetic trajectories in the unit tangent sphere bundle with pseudo-Riemannian g-natural metrics of a Riemannian manifold. A high interest is dedicated to the case when the base manifold is a space form and when the metric is of Kaluza–Klein type. Slant curves are obtained when a certain conservation law is satisfied. We give a complete classification of slant magnetic curves (respectively, geodesics) on $$T_1M$$ , when M is a two-dimensional Riemannian manifold of constant curvature.