Research Article
BibTex RIS Cite
Year 2023, Volume: 16 Issue: 1, 181 - 195, 30.04.2023
https://doi.org/10.36890/iejg.1243521

Abstract

References

  • [1] Anosov, D. V., Sinaĭ, Y. G.: Some smooth ergodic systems, Uspekhi Mat. Nauk. 22 (5), 107–172 (1967). English translation: Russ. Math. Surv. 22 (5), 103–167 (1967).
  • [2] Arnol’d, V. I.: Some remarks on flows of line elements and frames. Dokl. Akad. Nauk. SSSR. 138, 255–257 (1961). English translation: Sov. Math. Dokl. 2, 562–564 (1961).
  • [3] Arnol’d, V. I.: First steps in symplectic topology. Uspekhi Mat. Nauk. 41 (6), 3–18 (1986). English translation: Russ. Math. Surv. 41, 1–21 (1986).
  • [4] Druţă-Romaniuc, S. L., Inoguchi, J., Munteanu, M. I.: Killing slant magnetic curves in the 3-dimensional Heisenberg group Nil3. Int. J. Geom. Methods Mod. Phys., Online Ready 2350094 (2023), https://doi.org/10.1142/S0219887823500949.
  • [5] Druţă-Romaniuc, S. L., Inoguchi, J., Munteanu, M. I., Nistor, A. I.: Magnetic curves in Sasakian manifolds. J. Nonlinear Math. Phys. 22 (3), 428–447 (2015).
  • [6] Druţă-Romaniuc, S. L., Munteanu, M. I.: Magnetic curves corresponding to Killing magnetic fields in E3. J. Math. Phys. 52, 113506 (2011).
  • [7] Duggal, K. L.: Geometry developed by the electromagnetic tensor field. Ann. Mat. Pura Appl. 119 (4), 239–245 (1979).
  • [8] Duggal, K. L.: Einstein-Maxwell equations compatible with certain Killing vectors with light velocity. Ann. Mat. Pura Appl. 120 (4), 263–268 (1979).
  • [9] Duggal, K. L.: On the four-current source of the electromagnetic fields. Ann. Mat. Pura Appl. 120 (4), 305–313 (1979).
  • [10] Duggal, K. L.: On Einstein-Maxwell field equations. Tensor. 34 (2), 199–204 (1980).
  • [11] Duggal, K. L.: On the geometry of electromagnetic fields of second class. Indian J. Pure Appl. Math. 14 (4), 455–461 (1983).
  • [12] Erjavec, Z.: On Killing magnetic curves in Sl(2, R) geometry. Rep. Math. Phys. 84 (3), 333–350 (2019).
  • [13] Erjavec, Z., Inoguchi, J.: Killing magnetic curves in Sol space. Math. Phys. Anal. Geom. 21, Article number 15, (2018).
  • [14] Erjavec, Z., Inoguchi, J.: J-trajectories in 4-dimensional solvable Lie group Sol40. Math. Phys. Anal. Geom. 25, Article number 8, (2022).
  • [15] Erjavec, Z., Inoguchi, J.: J-trajectories in 4-dimensional solvable Lie group Sol41. submitted.
  • [16] Erjavec, Z., Klemenˇci´c, D., Bosak, M.: On Killing magnetic curves in hyperboloid model of SL(2, R) geometry. Sarajevo J. Math., to appear.
  • [17] Ginzburg, V. L.: A charge in a magnetic field: Arnold’s problems 1981-9, 1982-24, 1984-4, 1994-14, 1994-35, 1996-17,1996-18, in Arnold’s problems (V.I. Arnold ed.) Springer-Verlag and Phasis, 395–401 (2004).
  • [18] Ikawa, O.: Motion of charged particles in homogeneous Kähler and homogeneous Sasakian manifolds. Far East J. Math. Sci. 14 (3), 283–302 (2004).
  • [19] Inoguchi, J., Munteanu, M. I.: Periodic magnetic curves in Berger spheres. Tohoku Math. J. 69 (1), 113–128 (2017).
  • [20] Inoguchi, J., Munteanu, M. I.: Magnetic curves in the real special linear group. Adv. Theor. Math. Phys. 23 (8), 2161–2205 (2019).
  • [21] Inoguchi, J., Munteanu, M. I.: Slant curves and magnetic curves. In: Contact geometry of slant submanifolds, Springer, Singapore, 199–259 (2022).
  • [22] Kobayashi, S., Nomizu, K.: Foundations of Differential Geometry. Vol II. Interscience Publishers. (1969).
  • [23] Kowalski, O., Vanhecke, L., Riemannian manifolds with homogeneous geodesics. Boll. Un. Mat. Ital. B 5 (7), 189–246 (1991).
  • [24] Munteanu, M. I., Nistor, A. I.: The classification of Killing magnetic curves in S2 × R. J. Geom. Phys. 62 (2), 170–182 (2012).
  • [25] Nistor, A. I.: Motion of charged particles in a Killing magnetic field in H2 × R. Rend. Sem. Mat. Univ. Politec. Torino. 73/1 (3-4), 161–170 (2016).
  • [26] O’Neill, B.: Semi-Riemannian Geometry with Applications to Relativity. Academic Press. London. (1983).
  • [27] Scott, P.: The geometries of 3-manifolds. Bull. London Math. Soc. 15, 401-487 (1983).
  • [28] Thurston, W. M.: Three-dimensional Geometry and Topology I. Princeton Math. Series. 35, (1997).

Killing Magnetic Curves in $\: \mathbb{H}^{3}$

Year 2023, Volume: 16 Issue: 1, 181 - 195, 30.04.2023
https://doi.org/10.36890/iejg.1243521

Abstract

We consider magnetic curves corresponding to the Killing magnetic fields in hyperbolic 3-space.

References

  • [1] Anosov, D. V., Sinaĭ, Y. G.: Some smooth ergodic systems, Uspekhi Mat. Nauk. 22 (5), 107–172 (1967). English translation: Russ. Math. Surv. 22 (5), 103–167 (1967).
  • [2] Arnol’d, V. I.: Some remarks on flows of line elements and frames. Dokl. Akad. Nauk. SSSR. 138, 255–257 (1961). English translation: Sov. Math. Dokl. 2, 562–564 (1961).
  • [3] Arnol’d, V. I.: First steps in symplectic topology. Uspekhi Mat. Nauk. 41 (6), 3–18 (1986). English translation: Russ. Math. Surv. 41, 1–21 (1986).
  • [4] Druţă-Romaniuc, S. L., Inoguchi, J., Munteanu, M. I.: Killing slant magnetic curves in the 3-dimensional Heisenberg group Nil3. Int. J. Geom. Methods Mod. Phys., Online Ready 2350094 (2023), https://doi.org/10.1142/S0219887823500949.
  • [5] Druţă-Romaniuc, S. L., Inoguchi, J., Munteanu, M. I., Nistor, A. I.: Magnetic curves in Sasakian manifolds. J. Nonlinear Math. Phys. 22 (3), 428–447 (2015).
  • [6] Druţă-Romaniuc, S. L., Munteanu, M. I.: Magnetic curves corresponding to Killing magnetic fields in E3. J. Math. Phys. 52, 113506 (2011).
  • [7] Duggal, K. L.: Geometry developed by the electromagnetic tensor field. Ann. Mat. Pura Appl. 119 (4), 239–245 (1979).
  • [8] Duggal, K. L.: Einstein-Maxwell equations compatible with certain Killing vectors with light velocity. Ann. Mat. Pura Appl. 120 (4), 263–268 (1979).
  • [9] Duggal, K. L.: On the four-current source of the electromagnetic fields. Ann. Mat. Pura Appl. 120 (4), 305–313 (1979).
  • [10] Duggal, K. L.: On Einstein-Maxwell field equations. Tensor. 34 (2), 199–204 (1980).
  • [11] Duggal, K. L.: On the geometry of electromagnetic fields of second class. Indian J. Pure Appl. Math. 14 (4), 455–461 (1983).
  • [12] Erjavec, Z.: On Killing magnetic curves in Sl(2, R) geometry. Rep. Math. Phys. 84 (3), 333–350 (2019).
  • [13] Erjavec, Z., Inoguchi, J.: Killing magnetic curves in Sol space. Math. Phys. Anal. Geom. 21, Article number 15, (2018).
  • [14] Erjavec, Z., Inoguchi, J.: J-trajectories in 4-dimensional solvable Lie group Sol40. Math. Phys. Anal. Geom. 25, Article number 8, (2022).
  • [15] Erjavec, Z., Inoguchi, J.: J-trajectories in 4-dimensional solvable Lie group Sol41. submitted.
  • [16] Erjavec, Z., Klemenˇci´c, D., Bosak, M.: On Killing magnetic curves in hyperboloid model of SL(2, R) geometry. Sarajevo J. Math., to appear.
  • [17] Ginzburg, V. L.: A charge in a magnetic field: Arnold’s problems 1981-9, 1982-24, 1984-4, 1994-14, 1994-35, 1996-17,1996-18, in Arnold’s problems (V.I. Arnold ed.) Springer-Verlag and Phasis, 395–401 (2004).
  • [18] Ikawa, O.: Motion of charged particles in homogeneous Kähler and homogeneous Sasakian manifolds. Far East J. Math. Sci. 14 (3), 283–302 (2004).
  • [19] Inoguchi, J., Munteanu, M. I.: Periodic magnetic curves in Berger spheres. Tohoku Math. J. 69 (1), 113–128 (2017).
  • [20] Inoguchi, J., Munteanu, M. I.: Magnetic curves in the real special linear group. Adv. Theor. Math. Phys. 23 (8), 2161–2205 (2019).
  • [21] Inoguchi, J., Munteanu, M. I.: Slant curves and magnetic curves. In: Contact geometry of slant submanifolds, Springer, Singapore, 199–259 (2022).
  • [22] Kobayashi, S., Nomizu, K.: Foundations of Differential Geometry. Vol II. Interscience Publishers. (1969).
  • [23] Kowalski, O., Vanhecke, L., Riemannian manifolds with homogeneous geodesics. Boll. Un. Mat. Ital. B 5 (7), 189–246 (1991).
  • [24] Munteanu, M. I., Nistor, A. I.: The classification of Killing magnetic curves in S2 × R. J. Geom. Phys. 62 (2), 170–182 (2012).
  • [25] Nistor, A. I.: Motion of charged particles in a Killing magnetic field in H2 × R. Rend. Sem. Mat. Univ. Politec. Torino. 73/1 (3-4), 161–170 (2016).
  • [26] O’Neill, B.: Semi-Riemannian Geometry with Applications to Relativity. Academic Press. London. (1983).
  • [27] Scott, P.: The geometries of 3-manifolds. Bull. London Math. Soc. 15, 401-487 (1983).
  • [28] Thurston, W. M.: Three-dimensional Geometry and Topology I. Princeton Math. Series. 35, (1997).
There are 28 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Article
Authors

Zlatko Erjavec 0000-0002-9402-1069

Jun-ichi Inoguchi 0000-0002-6584-5739

Publication Date April 30, 2023
Acceptance Date April 8, 2023
Published in Issue Year 2023 Volume: 16 Issue: 1

Cite

APA Erjavec, Z., & Inoguchi, J.-i. (2023). Killing Magnetic Curves in $\: \mathbb{H}^{3}$. International Electronic Journal of Geometry, 16(1), 181-195. https://doi.org/10.36890/iejg.1243521
AMA Erjavec Z, Inoguchi Ji. Killing Magnetic Curves in $\: \mathbb{H}^{3}$. Int. Electron. J. Geom. April 2023;16(1):181-195. doi:10.36890/iejg.1243521
Chicago Erjavec, Zlatko, and Jun-ichi Inoguchi. “Killing Magnetic Curves in $\: \mathbb{H}^{3}$”. International Electronic Journal of Geometry 16, no. 1 (April 2023): 181-95. https://doi.org/10.36890/iejg.1243521.
EndNote Erjavec Z, Inoguchi J-i (April 1, 2023) Killing Magnetic Curves in $\: \mathbb{H}^{3}$. International Electronic Journal of Geometry 16 1 181–195.
IEEE Z. Erjavec and J.-i. Inoguchi, “Killing Magnetic Curves in $\: \mathbb{H}^{3}$”, Int. Electron. J. Geom., vol. 16, no. 1, pp. 181–195, 2023, doi: 10.36890/iejg.1243521.
ISNAD Erjavec, Zlatko - Inoguchi, Jun-ichi. “Killing Magnetic Curves in $\: \mathbb{H}^{3}$”. International Electronic Journal of Geometry 16/1 (April 2023), 181-195. https://doi.org/10.36890/iejg.1243521.
JAMA Erjavec Z, Inoguchi J-i. Killing Magnetic Curves in $\: \mathbb{H}^{3}$. Int. Electron. J. Geom. 2023;16:181–195.
MLA Erjavec, Zlatko and Jun-ichi Inoguchi. “Killing Magnetic Curves in $\: \mathbb{H}^{3}$”. International Electronic Journal of Geometry, vol. 16, no. 1, 2023, pp. 181-95, doi:10.36890/iejg.1243521.
Vancouver Erjavec Z, Inoguchi J-i. Killing Magnetic Curves in $\: \mathbb{H}^{3}$. Int. Electron. J. Geom. 2023;16(1):181-95.

Cited By

Conformal trajectories in three-dimensional space forms
International Journal of Geometric Methods in Modern Physics
https://doi.org/10.1142/S021988782450258X