On Magnetic Curves According to Killing Vector Fields in Euclidean 3-Space

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M. Khalifa Saad
H. S. Abdel-Aziz
Haytham A. Ali

Abstract

In the geometric theory of space curves, a magnetic field generates magnetic flow. The trajectories of magnetic flow are called magnetic curves. In the present paper, we obtain magnetic curves corresponding to killing magnetic fields in Euclidean 3-space E3. The magnetic curves of the spherical indicatrices of the tangent, principal normal and binormal for a regular space curve are said to be meant curves. Also, we investigate the magnetic curves of the tangent indicatrix and obtain the trajectories of the magnetic fields called TT-magnetic, NT-magnetic and BT-magnetic curves. Finally, some computational examples in support of our main results are given and plotted.

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