Pseudo null curve variations for Bishop frame in 3D semi-Riemannian manifold

Abstract

In the present paper, the relation between invariants of the pseudo null curves and the variational vector fields of semi-Riemannian manifolds is introduced. After that, the Killing equations are written in terms of the Bishop curvatures along the pseudo null curve. By means of this approach, Killing equations make allow to interpret the movement of charged particles within the magnetic field. Afterwards, as an application, pseudo null magnetic curves are defined using the Killing variational vector field. The parametric representations of all pseudo null magnetic curves are determined in semi-Riemannian space form. Moreover, various examples of pseudo null magnetic curves are illustrated.