Surveys in Mathematics and its Applications

ISSN 1842-6298 (electronic), 1843-7265 (print)
 Volume 15 (2020), 139 -- 151

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.

MAGNETIC AND SLANT CURVES IN KENMOTSU MANIFOLDS

P. K. Pandey and S. Mohammad

Abstract. Motivated by the recent studies of the magnetic curves in quasi-Sasakian, Sasakian, and Cosymplectic manifolds, in this article we investigate the magnetic trajectories with respect to contact magnetic fields in Kenmotsu manifolds. Moreover, we study the slant curves, torsion and curvature in Kenmotsu manifolds.

2020 Mathematics Subject Classification: 53C15, 53C25.
Keywords: Magnetic curves, Slant curves, Kenmotsu manifold.

Full text

References

  1. T. Adachi, Kahler magnetic fields on a complex projective space, Proc. Japan Acad., Series A, Math. Sci., 70(1) (1994), 12-13. MR1272661. Zbl 0797.53018.

  2. T. Adachi, Kahler magnetic fields on a Kahler manifold of negative curvature, Diff. Geom. Appl., 29 (2011), S2-S8. MR2831993. Zbl 1228.53050.

  3. M. Barros, A. Romero, Magnetic vortices, EPL(Europhysics Letters), 77(3) (2007), p.34002.

  4. M. Barros, J. L. Cabrerizo, M. Fernandez and A. Romero, Magnetic vortex filament flows, J. Math. Phys., 48(8) (2007), p.082904. MR2349410. Zbl 1152.81329.

  5. D. E. Blair, Riemannian geometry of contact and symplectic manifolds, Progress in Math. 203, Birkhauser, Boston-Basel-Berlin, 2002. MR1874240. Zbl 1011.53001.

  6. J. L. Cabrerizo, Magnetic fields in 2D and 3D sphere, J. Nonlinear Math. Phy., 20(3) (2013), 440-450. MR3196453. Zbl 1420.53032.

  7. J. L. Cabrerizo, M. Fernandez and J. S. Gomez, On the existence of almost contact structure and the contact magnetic field, Acta Math. Hungar., 125(1-2) (2009), 191-199. MR2564430. Zbl 1212.53112.

  8. C. Calin, M. Crasmareanu and M. Munteanu, Slant curves in 3-dimensional f -Kenmotsu manifolds, J. Math. Anal. Appl. 394 (2012), 400--407. MR2926230. Zbl 1266.53056.

  9. J. T. Cho, J. I. Inoguchi and J. E. Lee, On slant curves in Sasakian 3-manifolds, Bull. Austral. Math. Soc., 74(3) (2006), 359-367. MR2273746. Zbl 1106.53013.

  10. S. L. Druta-Romaniuc, M. I. Munteanu, Magnetic curves corresponding to Killing magnetic fields in E3, J. Math. Phy., 52(11) (2011), 113506. MR2906576. Zbl 1272.37020.

  11. S. L. Druta-Romaniuc, J. I. Inoguchi, M. I. Munteanu and A. I. Nistor, Magnetic curves in Sasakian manifolds, J. Nonlinear Math. Phy., 22(3) (2015), 428-447. MR3378108. Zbl 1420.53035.

  12. S. L. Druta-Romaniuc, J. I. Inoguchi, M. I. Munteanu and A. I. Nistor, Magnetic curves in cosymplectic manifolds, Reports on Math. Phy., 78(1) (2016), 33-48. MR3542529. Zbl 1353.53033.

  13. S. Guvenc, C. Ozgur, On slant magnetic curves in S-manifolds, J. Nonlinear Math. Phy., 26(4) (2019), 536-554. MR3978634. Zbl 1418.53053.

  14. O. Ikawa, Motion of charged particles in Sasakian manifolds, Sut J. Math., 43(2) (2007), 263-266. MR2417544. Zbl 1143.78002.

  15. O. Ikawa, Motion of charged particles from the geometric view point, J. Geom. Symmetry Phys., 18 (2010), 23-47. MR2668881. Zbl 1203.53019.

  16. O. Ikawa, Motion of charged particles in two-step Nilpotent Lie Groups, J. Geom. Symmetry Phys., 20 (2010), 57-67. MR2780241. Zbl 1382.53008.

  17. J. I. Inoguchi, J. E. Lee, Slant curves in 3-dimensional almost f-Kenmotsu manifolds, Commun. Korean Math. Soc., 32(2) (2017), 417-424. MR3641176. Zbl 1375.53041.

  18. J. I. Inoguchi, M. I. Munteanu and A. I. Nistor, Magnetic curves in quasi-Sasakian 3-manifolds, Anal. Math. Phy., 9(1) (2019), 43-61. MR3933526. Zbl 1417.53033.

  19. K. Kenmotsu, A class of almost contact Riemannian manifolds, Tohoku Math. J., 24(1) (1972), 93-103. MR0319102. Zbl 0245.53040.

  20. D. A. Kalinin, Trajectories of charged particles in Kahler magnetic fields, Reports on Math. Phy., 39(3) (1997), 299-309. MR1477896. Zbl 0896.58031.

  21. M. I. Munteanu, A. I. Nistor, The classification of Killing magnetic curves in \mathbbS2× ℝ, J. Geom. Phy., 62(2) (2012), 170-182. MR2864469. Zbl 1239.78003.

  22. Z. Ozdemir, I. Gok, Y. Yayli and F. N. Ekmekci, Notes on magnetic curves in 3D semi-Riemannian manifolds, Turk. J. Math., 39(3) (2015), 412-426. MR3343494. Zbl 1345.53025.




Pradeep Kumar Pandey
Department of Mathematics, Jaypee University of Information Technology,
Solan - 173234, Himachal Pradesh, India.
e-mail: pandeypkdelhi@gmail.com

Sameer Mohammad
Department of Mathematics, Jaypee University of Information Technology,
Solan - 173234, Himachal Pradesh, India.
e-mail: sksameer08@gmail.com





http://www.utgjiu.ro/math/sma