Acknowledgement
The authors would like to thank the referee for her/his careful reading of the manuscript and suggestions for improving this article. The authors would also like to acknowledge professor Shimpei Kobayashi and Marian Ioan Munteanu for their useful suggestions. The second named author is partially supported by JSPS KAKENHI Grant Number 19K03461.
References
- S. L. Druta-Romaniuc, J. 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
- S. L. Druta-Romaniuc, J. Inoguchi, M. I. Munteanu, and A. I. Nistor, Magnetic curves in cosymplectic manifolds, Rep. Math. Phys. 78 (2016), no. 1, 33-48. https://doi.org/10.1016/S0034-4877(16)30048-9
- Z. Erjavec, On Killing magnetic curves in SL(2, ℝ) geometry, Rep. Math. Phys. 84 (2019), no. 3, 333-350. https://doi.org/10.1016/S0034-4877(19)30096-5
- Z. Erjavec and J. Inoguchi, Magnetic curves in Sol3, J. Nonlinear Math. Phys. 25 (2018), no. 2, 198-210. https://doi.org/10.1080/14029251.2018.1452670
- Z. Erjavec and J. Inoguchi, Killing magnetic curves in Sol space, Math. Phys. Anal. Geom. 21 (2018), no. 2, Paper No. 15, 15 pp. https://doi.org/10.1007/s11040-018-9272-6
- Z. Erjavec and J. Inoguchi, On magnetic curves in almost cosymplectic Sol space, Results Math. 75 (2020), no. 3, Paper No. 113, 16 pp. https://doi.org/10.1007/s00025-020-01235-y
- R. Filipkiewicz, Four dimensional geometries, Ph. D. Thesis, University of Warwick, 1983.
- J. Inoguchi and M. I. Munteanu, Magnetic curves in the real special linear group, Adv. Theor. Math. Phys. 23 (2019), no. 8, 2161-2205. https://doi.org/10.4310/ATMP.2019.v23.n8.a6
- D. A. Kalinin, Trajectories of charged particles in Kahler magnetic fields, Rep. Math. Phys. 39 (1997), no. 3, 299-309. https://doi.org/10.1016/S0034-4877(97)89750-9
-
M. I. Munteanu and A. I. Nistor, The classification of Killing magnetic curves in
$\mathbb{S}^2{\times}\mathbb{R}$ , J. Geom. Phys. 62 (2012), no. 2, 170-182. https://doi.org/10.1016/j.geomphys.2011.10.002 - A. I. Nistor, Motion of charged particles in a Killing magnetic field in ℍ2 × ℝ, Rend. Semin. Mat. Univ. Politec. Torino 73 (2015), no. 1, 161-170.
- T. Oguro and K. Sekigawa, Almost Kahler structures on the Riemannian product of a 3-dimensional hyperbolic space and a real line, Tsukuba J. Math. 20 (1996), no. 1, 151-161. https://doi.org/10.21099/tkbjm/1496162985
- C. T. C. Wall, Geometries and geometric structures in real dimension 4 and complex dimension 2, in Geometry and topology (College Park, Md., 1983/84), 268-292, Lecture Notes in Math., 1167, Springer, Berlin, 1985. https://doi.org/10.1007/BFb0075230
- C. T. C. Wall, Geometric structures on compact complex analytic surfaces, Topology 25 (1986), no. 2, 119-153. https://doi.org/10.1016/0040-9383(86)90035-2