Magnetic Frenet curves on para-Sasakian manifolds

Abstract

The study of magnetic curves, seen as solutions of Lorentz equation, has been done mainly in 3-dimensional case, motivated by theoretical physics. Then it was extended in higher dimensions, as for instance in K\"alerian or Sasakian frame. This paper deals for the first time in literature with magnetic Frenet curves in higher dimensional paracontact context. Several classifications are provided here for different type of magnetic curves on para-Sasakian manifolds. Some relations between magnetic Frenet curves and Lorenz force are obtained on these spaces and examples of magnetic curves associated to paracontact magnetic fields are constructed. Some explicit equations of the paracontact magnetic curves on the para-Sasakian manifold $(\mathbb{R}^{2n+1},\varphi,\xi,\eta,g)$ are given at the end.