Some Properties of Special Magnetic Curves

Article Sidebar

PDF
Cite as:
H. S. Abdel-Aziz, M. Khalifa Saad, Haytham A. Ali, Some Properties of Special Magnetic Curves, Int. J. Anal. Appl., 16 (2) (2018), 193-208.

Main Article Content

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

Abstract

In the theory of curves, a magnetic field generates a magnetic flow whose trajectories are curves called magnetic curves. This paper aims at studying some properties for these curves which corresponding to the Killing magnetic fields in the 3-dimensional Euclidean space. We investigate the trajectories of the magnetic fields called $T$-magnetic and $e$-magnetic curves, also we give some characterizations of these curves. In addition, we determine all magnetic curves for new spherical images of a spherical curve and finally, we defray some examples to confirm our main results.

Article Details

References

  1. R. Talman, Geometric Mechanics, Toward a Unification of Classical Physics, second ed., Wiley-VCH, 2007.
  2. A. Comtet, On the Landau levels on the hyperbolic plane, Ann. Physics 173 (1987), 185-209.
  3. T. Sunada, Magnetic flows on a Riemann surface, in: Proceedings of KAIST Mathematics Workshop, (1993), 93-108.
  4. T. Adachi, Kähler magnetic field on a complex projective space, Proc. Japan Acad. Ser. A Math. Sci. 70 (1994), 12-13.
  5. T. Adachi, Kähler magnetic flow for a manifold of constant holomorphic sectional curvature, Tokyo J. Math. 18 (2) (1995), 473-483.
  6. J.L. Cabrerizo, M. Fernández, J.S. Gómez, The contact magnetic flow in 3D Sasakian manifolds, J. Phys. A 42 (19) (2009), 1-10.
  7. J.L. Cabrerizo, M. Fernández, J.S. Gómez, On the existence of almost contact structure and the contact magnetic field, Acta Math. Hungar. 125 (1-2) 30 (2009), 191-199.
  8. S.L. Drut ¸˘ a-Romaniuc, M.I. Munteanu, Magnetic curves corresponding to Killing magnetic fields in E 3 , J. Math. Phys. 52 (11) (2011), 1-11.
  9. M.I. Munteanu, A.I. Nistor, The classification of Killing magnetic curves in S 2 ×R, J. Geom. Phys. 62 (2) (2012), 170-182.
  10. M. Barros, A. Romero, Magnetic vortices, Europhys. Lett. 77 (2007), 1-5.
  11. J. Koenderink, Solid shape, MIT Press, Cambridge, MA, (1990).
  12. L. Chen, Q. Han, D. Pei, W. Sun, The singularities of null surfaces in anti de Sitter 3-space, J. Math. Anal. Appl., 366 (2010), 256-265.
  13. B. O'Neil, Semi-Riemannian geometry, With applications to relativity, Academic Press, Inc., New York, (1983).
  14. M. Barros, J. L. Cabrerizo, M. Fernández and A. Romero, Magnetic vortex filament flows, J Math Phys 48 (2007), 1-27.
  15. Ë™ I. Arslan and H.H. Hacisaliho˘ glu, On the spherical representatives of a curve, Int. J. Contemp. Math. Sciences, 4 (34) (2009), 1665-1670.
  16. S. Yilmaz, Bishop spherical images of a spacelike curve in Minkowski 3-space, Int. J. Phys. Scien., 5 (6), (2010), 898-905.
  17. S. Yilmaz, E. ¨ Ozyilmaz and M. Turgut, New spherical indicatrices and their characterizations, An. S ¸t. Univ. Ovidius Constanta, 18 (2) (2010), 337-354.