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Magnetic Curves in C-manifolds

Year 2022, Volume: 15 Issue: 1, 145 - 152, 30.04.2022
https://doi.org/10.36890/iejg.948817

Abstract

In this paper, we study normal magnetic curves in $C$-manifolds. We prove that magnetic trajectories with respect to the contact magnetic fields are
indeed $\theta _{\alpha }$-slant curves with certain curvature functions. Then, we give the parametrizations of normal magnetic curves in $\mathbb{R}^{2n+s}$ with its structures as a $C$-manifold.

References

  • Adachi ,T.: Curvature bound and trajectories for magnetic fields on a Hadamard surface. Tsukuba J. Math. 20, 225–230, (1996).
  • Barros M., Romero, A., Cabrerizo, J. L., Fernandez, M.: The Gauss-Landau-Hall problem on Riemannian surfaces. J. Math. Phys. 46, no. 11, 112905, 15 pp, (2005).
  • Blair, D. E.: Geometry of manifolds with structural group U (n) × O(s). J. Differential Geom- etry, 4, 155-167, (1970).
  • Blair, D. E.: Riemannian Geometry of Contact and Symplectic Manifolds, 2nd ed., Progr. Math. 203, Birkhiiuser Boston, Boston, MA, 2010.
  • Comtet, A.: On the Landau levels on the hyperbolic plane. Ann. Physics 173, 185-209, (1987).
  • Druta-Romaniuc, S. L., Inoguchi, J., Munteanu, M. I., Nistor, A. I.: Magnetic curves in Sasakian manifolds. Journal of Nonlinear Mathematical Physics, 22, 428-447, (2015).
  • Güvenç, Ş., Özgür, C.: On slant magnetic curves in S-manifolds. J. Nonlinear Math. Phys. 26 (4), 536–554, (2019).
  • Druta-Romaniuc, S.-L., Inoguchi, J.-I., Munteanu, M. I., Nistor, A. I.: Magnetic Curves in Cosymplectic Manifolds. Reports on Mathematical Physics. 78 (1), 33-48, (2016).
Year 2022, Volume: 15 Issue: 1, 145 - 152, 30.04.2022
https://doi.org/10.36890/iejg.948817

Abstract

References

  • Adachi ,T.: Curvature bound and trajectories for magnetic fields on a Hadamard surface. Tsukuba J. Math. 20, 225–230, (1996).
  • Barros M., Romero, A., Cabrerizo, J. L., Fernandez, M.: The Gauss-Landau-Hall problem on Riemannian surfaces. J. Math. Phys. 46, no. 11, 112905, 15 pp, (2005).
  • Blair, D. E.: Geometry of manifolds with structural group U (n) × O(s). J. Differential Geom- etry, 4, 155-167, (1970).
  • Blair, D. E.: Riemannian Geometry of Contact and Symplectic Manifolds, 2nd ed., Progr. Math. 203, Birkhiiuser Boston, Boston, MA, 2010.
  • Comtet, A.: On the Landau levels on the hyperbolic plane. Ann. Physics 173, 185-209, (1987).
  • Druta-Romaniuc, S. L., Inoguchi, J., Munteanu, M. I., Nistor, A. I.: Magnetic curves in Sasakian manifolds. Journal of Nonlinear Mathematical Physics, 22, 428-447, (2015).
  • Güvenç, Ş., Özgür, C.: On slant magnetic curves in S-manifolds. J. Nonlinear Math. Phys. 26 (4), 536–554, (2019).
  • Druta-Romaniuc, S.-L., Inoguchi, J.-I., Munteanu, M. I., Nistor, A. I.: Magnetic Curves in Cosymplectic Manifolds. Reports on Mathematical Physics. 78 (1), 33-48, (2016).
There are 8 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Article
Authors

Şaban Güvenç 0000-0001-6254-4693

Early Pub Date April 30, 2022
Publication Date April 30, 2022
Acceptance Date December 7, 2021
Published in Issue Year 2022 Volume: 15 Issue: 1

Cite

APA Güvenç, Ş. (2022). Magnetic Curves in C-manifolds. International Electronic Journal of Geometry, 15(1), 145-152. https://doi.org/10.36890/iejg.948817
AMA Güvenç Ş. Magnetic Curves in C-manifolds. Int. Electron. J. Geom. April 2022;15(1):145-152. doi:10.36890/iejg.948817
Chicago Güvenç, Şaban. “Magnetic Curves in C-Manifolds”. International Electronic Journal of Geometry 15, no. 1 (April 2022): 145-52. https://doi.org/10.36890/iejg.948817.
EndNote Güvenç Ş (April 1, 2022) Magnetic Curves in C-manifolds. International Electronic Journal of Geometry 15 1 145–152.
IEEE Ş. Güvenç, “Magnetic Curves in C-manifolds”, Int. Electron. J. Geom., vol. 15, no. 1, pp. 145–152, 2022, doi: 10.36890/iejg.948817.
ISNAD Güvenç, Şaban. “Magnetic Curves in C-Manifolds”. International Electronic Journal of Geometry 15/1 (April 2022), 145-152. https://doi.org/10.36890/iejg.948817.
JAMA Güvenç Ş. Magnetic Curves in C-manifolds. Int. Electron. J. Geom. 2022;15:145–152.
MLA Güvenç, Şaban. “Magnetic Curves in C-Manifolds”. International Electronic Journal of Geometry, vol. 15, no. 1, 2022, pp. 145-52, doi:10.36890/iejg.948817.
Vancouver Güvenç Ş. Magnetic Curves in C-manifolds. Int. Electron. J. Geom. 2022;15(1):145-52.