Magnetic trajectories on tangent sphere bundle with g-natural metrics

Natural Paracontact Magnetic Trajectories on Unit Tangent Bundles

“…paracontact) magnetic field. In [1], the authors considered contact magnetic fields that are associated to the family of g-natural contact metric structures on the unit tangent bundle of a Riemannian manifold (cf. [2]) and studied the corresponding contact magnetic trajectories (we also refer to [3,4] for the Sasaki metric case).…”

“…In [1], the authors gave the classification of geodesics on unit tangent bundles of constant Gaussian curvature surfaces endowed with pseudo-Riemannian Kaluza-Klein type metrics, except in the case when the Gaussian curvature is negative equal to a+c a . As a consequence of Theorem 3, we have the following corollaries that extend the classification of geodesics to the case k = a+c a < 0:…”

Geodesics and natural complex magnetic trajectories on tangent bundles

“…paracontact) structures had been recently made by the authors and M.I. Munteanu [1] (resp. by the authors [2]).…”

“…Magnetic curves represent, in Physics, the trajectories of charged particles moving on a Riemannian manifold under the action of a magnetic field. A magnetic field F on a Riemannian manifold (M, g) is any closed 2−form F and the Lorentz-force associated to F is an endomorphism field φ such that F (X, Y ) = g(φ(X), Y ), (1) for all X, Y ∈ X(M ). The magnetic trajectories of F are curves γ in M that satisfy the Lorentz equation (called also the Newton equation)…”