Abstract
We investigate some geometrical properties of magnetic curves in S3 under the action of the Killing magnetic field V=a∂x+ b∂y+ c∂z. The other main result is provided about the classification of the equations of the geodesics in S3. Moreover, some most relevant graphs of the main results were drawn in this paper.
Highlights
The study of magnetic fields and their corresponding magnetic curves on different manifolds is one of the important research topics between differential geometry and physics
We investigate some geometrical properties of magnetic curves in S3 under the action of the Killing magnetic field V = a∂x + b∂y + c∂z
The magnetic curves on the Riemannian manifolds are trajectories of charged particles moving on M under the magnetic field
Summary
The study of magnetic fields and their corresponding magnetic curves on different manifolds is one of the important research topics between differential geometry and physics. Corresponding to parallel Lorentz forces, the magnetic trajectories are obtained on some 2-dimensional space [1, 2]. The classification of the magnetic curves in 3dimensional Minkowski space with Killing magnetic field and in three-dimensional almost paracontact manifolds was given in [5, 6]. If we want to extend this concept to other ambient spaces, it is necessary to distinguish between the manifolds and the tangent vector spaces. The authors extend the rectifying theory and the relative results in the 3-dimensional sphere [13] Looking over all these results obtained in classification of magnetic trajectories corresponding to magnetic fields in different ambient spaces, until recently, and to the best of our knowledge, there has been little information available about the magnetic curves in the 3-dimensional sphere.
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