Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

ASSOCIATED CURVES OF CHARGED PARTICLE MOVING WITH THE EFFECT OF MAGNETIC FIELD

  • Received : 2022.04.26
  • Accepted : 2022.11.25
  • Published : 2023.04.30
Download PDF
⟨ Previous Next ⟩

Abstract

Magnetic curves are the trajectories of charged particals which are influenced by magnetic fields and they satisfy the Lorentz equation. It is important to find relationships between magnetic curves and other special curves. This paper is a study of magnetic curves and this kind of relationships. We give the relationship between β-magnetic curves and Mannheim, Bertrand, involute-evolute curves and we give some geometric properties about them. Then, we study this subject for γ-magnetic curves. Finally, we give an evaluation of what we did.

Keywords

References

  1. E. As and A. Sarioglugil, On the Bishop curvatures of involute-evolute curve couple in E3, Inter. J. Phys. Sci. 9 (2014), no. 7, 140-145.  https://doi.org/10.5897/IJPS2013.4079
  2. M. Bilici and Caliskan, On the involutes of the spacelike curve with a timelike binormal in Minkowski 3-space, Int. Math. Forum. 4 (2009), no. 31, 1497-1509. 
  3. Z. Bozkurt, I. Gok, Y. Yayli, and F. N. Ekmekci, A new approach for magnetic curves in 3D Riemannian manifolds, J. Math. Phys. 55 (2014), no. 5, 053501. 
  4. J. H. Choi and Y. H. Kim, Associated curves of a Frenet curve and their applications, Appl. Math. Comput. 218 (2012), no. 18, 9116-9124.  https://doi.org/10.1016/j.amc.2012.02.064
  5. S. L. Druta-Romaniuc, J. I. Inoguchi, M. I. Munteanu, and A. I Nistor, Magnetic curves in Sasakian manifolds, J. Nonlinear Math. Phys. 22 (2015), no. 3, 428-447.  https://doi.org/10.1080/14029251.2015.1079426
  6. S. L. Druta-Romaniuc and M. I. Munteanu, Magnetic curves corresponding to Killing magnetic fields in E3, J. Math. Phys. 52 (2011), no. 11, 113506. 
  7. N. Ekmekci and K. Ilarslan, On Bertrand curves and their characterization, Differ. Geom. Dyn. Syst. 3 (2001), no. 2, 17-24. 
  8. D. Fuchs, Evolutes and involutes of spatial curves, Amer. Math. Monthly 120 (2013), no. 3, 217-231. https://doi.org/10.4169/amer.math.monthly.120.03.217 
  9. T. Fukunaga and M. Takahashi, Evolutes and involutes of frontals in the Euclidean plane, Demonstratio Mathematica 48 (2015), no. 2, 147-166.  https://doi.org/10.1515/dema-2015-0015
  10. J. I. Inoguchi and M. I. Munteanu, Magnetic curves in the real special linear group, arXiv preprint arXiv:1811.11993. (2018).  https://doi.org/10.4310/ATMP.2019.v23.n8.a6
  11. S. Izumiya and N. Takeuchi, Generic properties of helices and Bertrand curves, J. Geom. 74 (2002). 
  12. M. Jleli and M. I. Munteanu, Magnetic curves on flat para-K ahler manifolds, Turkish J. Math. 39 (2015), no. 6, 963-969.  https://doi.org/10.3906/mat-1503-40
  13. G. U. Kaymanli, C. Ekici, and M. Dede, On the directional associated curves of timelike space curve, In Conference Proceedings of Science and Technology. 2 (2018), no. 3, 173-179. 
  14. T. Korpinar, On T-magnetic biharmonic particles with energy and angle in the three dimensional Heisenberg group H, Adv. Appl. Clifford Algebr. 28 (2018), no. 1, Paper No. 9, 15 pp. https://doi.org/10.1007/s00006-018-0834-2 
  15. T. Korpinar, A new version of normal magnetic force particles in 3D Heisenberg space, Adv. Appl. Clifford Algebr. 28 (2018), no. 4, Paper No. 83, 13 pp. https://doi.org/10.1007/s00006-018-0900-9 
  16. T. Korpinar, A new velocity magnetic particles with flows by spherical frame, Differ. Equ. Dyn. Syst. (2018), 1-7. 
  17. T. Korpinar, M. T. Sariaydin, and E. Turhan, Associated curves according to bishop frame in Euclidean 3-space, Adv. Model. Optimization 15 (2013), no. 3, 713-717. 
  18. H. Liu and F. Wang, Mannheim partner curves in 3-space, J. Geom. 88 (2008), no. 1-2, 120-126.  https://doi.org/10.1007/s00022-007-1949-0
  19. N. Macit and M. Duldul, Some new associated curves of a Frenet curve in E3 and E4, Turkish J. Math. 38 (2014), no. 6, 1023-1037.  https://doi.org/10.3906/mat-1401-85
  20. M. Masal and A. Z. Azak, Mannheim B-curve in the Euclidean 3-space, Kuwait J. Sci. 44 (2017), no. 1, 36-41. 
  21. H. Matsuda and S. Yorozu, Notes on Bertrand curves, ynu.repo.nii.ac.jp. (2003). 
  22. M. I. Munteanu, Magnetic curves in a Euclidean space: one example, several approaches, Publ. Inst. Math. (Beograd) (N.S.) 94(108) (2013), 141-150. https://doi.org/10.2298/PIM1308141M 
  23. S. K. Nurkan, I. A. Guven, and M. K. Karacan, Characterizations of adjoint curves in Euclidean 3-space, Proceedings of the National Academy of Sciences, India Section A: Physical Sciences 89 (2019), no. 1, 155-161.  https://doi.org/10.1007/s40010-017-0425-y
  24. B. O'Neill, Elementary Differential Geometry, revised second edition, Elsevier/Academic Press, Amsterdam, 2006. 
  25. K. Orbay and E. Kasap, On Mannheim partner curves in E3, Int. J. Phys. Sci. 4 (2009), no. 5, 261-264. 
  26. E. Ozyilmaz and S. Yilmaz, Involute-evolute curve couples in the Euclidean 4-space, Int. J. Open Problems Compt. Math. 2 (2009), no. 2, 168-174. 
  27. B. Sahiner, Some associated curves of binormal indicatrix of a curve in Euclidean 3-space, In 16 th International Geometry Symposium, p. 302, 2018. 
  28. B. Sahiner and M. Onder, Slant helices, Darboux helices and similar curves in dual space D3, Mathematica Moravica. 20 (2016), no. 1, 1.