A Geometric view of Magnetic Surfaces and Magnetic Curves

In the present paper, we approach the magnetic surfaces geometrically. For this aim, we study the

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  • [1] Barros, M., Romero, A., Magnetic vortices. EPL, 77(2007) 1-5.
  • [2] Barros, M., Cabrerizo, J.L., Fernandez,M., Romero, A., Magnetic vortex filament flows. J. Math. Phys.,48(8) (2007) 082904.
  • [3] Barros, M. General helices and a theorem of Lancret. Proc. Am.Math. Soc.,125, 1503-1509, 1997.
  • [4] Bird, B.R., Stewart, W.E., Lightfoot, E. N., Transport Phenomena. Wiley. ISBN 0-471-07392-X, 1960.
  • [5] Boozer, A.H., Physics of magnetically confined plasmas. Rev. Mod. Phys., DOI:https://doi.org/10.1103/RevModPhys.76.1071, 2005.
  • [6] Bozkurt, Z.,Gök, İ., Yaylı Y., Ekmekci, F.N., A new Approach for Magnetic Curves in Riemannian 3D?Manifolds. J. Math. Phys., 55(2014), 1-12.
  • [7] Cabrerizo, J.L., Magnetic fields in 2D and 3D sphere. J. Nonlinear Math. Phys., 20(3)(2013), 440-4503.
  • [8] Dru¸t-Romaniuc, S.L., Munteanu, M.I., Magnetic curves corresponding to Killing magnetic fields in E3. J. Math. Phys.,52(2011), 113506,
  • [9] Hazeltine, R.D., Meiss, J. D. Plasma Confinement. Dover publications. inc. Mineola, New York, 2003.
  • [10] Pedersen, T.S., Boozer, A.H., Confinement of nonneutral plasmas on magnetic surfaces. Phys. Rev. Lett., 88 (2002), 205002.
  • [11] Wang, G.J., Tang, K., Tai, C.L., Parametric representation of a surface pencil with a common spatial geodesic. Computer-Aided Design, 36(5)(2004), 447-459.
  • [12] Illert, C., Formulation and solution of the classical problem, II Tubular three dimensional surfaces. Nuovo Cimento, 11(1989), 761-780.