Physics

Gravitation

Mathematics

Mathematical physics

Manifold (fluid mechanics)

Magnetic field

Engineering

Mathematical analysis

Riemannian geometry

Geometry

Riemannian manifold

Quantum mechanics

Classical mechanics

Mechanical engineering

International Journal of Geometric Methods in Modern Physics

In this paper, we study a special type of magnetic trajectories associated with a magnetic field [Formula: see text] defined on a 3D Riemannian manifold. First, we assume that we have a moving charged particle which is supposed to be under the action of a gravitational force [Formula: see text] in the magnetic field [Formula: see text] on the 3D Riemannian manifold. Then, we determine trajectories of the charged particle associated with the magnetic field [Formula: see text] and we define gravitational magnetic curves ([Formula: see text]-magnetic curves) of the magnetic vector field [Formula: see text] on the 3D Riemannian manifold. Finally, we investigate some geometrical and physical features of the moving charged particle corresponding to the [Formula: see text]-magnetic curve. Namely, we compute the energy, magnetic force, and uniformity of the [Formula: see text]-magnetic curve.

Gravitational magnetic curves on 3D Riemannian manifolds