Ana-Irina Nistor
Gheorghe Asachi Technical University of Iaşi, Iaşi, Romania

The study of magnetic trajectories originates in Physics and they represent the trajectories of charged particles moving on a Riemannian manifold under the influence of an external magnetic field, given by a divergence-free vector field. In the absence of the magnetic field, the particle moves freely, describing the geodesics of the ambient space. After recalling some well-known results in the field, we study the magnetic geodesics as the solutions of the Lorentz equation defined by the cross product corresponding to the 7-dimensional Euclidean space. We find several examples of such trajectories and moreover, we motivate our results making a comparison with the 3-dimensional Euclidean case, ambient space which was among the first ones approached in the study of magnetic trajectories.