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Year 2024, , 147 - 152, 28.03.2024

Özgür Kelekçi

https://doi.org/10.17776/csj.1400543

Abstract

References

  • [1] Hinterleitner I., Mikes J., On F-planar mappings of spaces with affine connections, Note Mat., 27(1) (2007) 111–118.
  • [2] Cabrerizo J.L., Fernandez M., Gomez J., On the existence of almost contact structure and the contact magnetic field, Acta. Math. Hungar., 125 (2009) 191-199.
  • [3] Cabrerizo J.L., Fernandez M., Gomez J., The contact magnetic flow in 3D Sasakian manifolds, J. Phys. A: Math. Theor., 42(19) (2009) 195-201.
  • [4] Munteanu M. I., Nistor A.I., The classification of Killing magnetic curves in S2× R, J. Geom. Phys., 62(2) (2012) 170-182.
  • [5] Druţă-Romaniuc S.L., Inoguchi J., Munteanu M.I., Nistor A.I., Magnetic curves in Sasakian manifolds, J. Nonlinear Math. Phys., 22(3) (2015) 428–447.
  • [6] Druţă-Romaniuc S.L., Inoguchi J., Munteanu M.I., Nistor A.I., Magnetic curves in cosymplectic manifolds, Rep. Math. Phys., 78 (1) (2016) 33-48.
  • [7] Erjavec Z., Inoguchi, J., Magnetic curves in Sol3, J. Nonlinear Math. Phys., 25(2) (2018) 198-210.
  • [8] Inoguchi, J., Munteanu, M.I., Magnetic curves in the real special linear group, Adv. Theor. Math. Phys., 23 (8) (2019) 2161-2205.
  • [9] Kelekçi Ö., Dündar F.S., Ayar G., Classification of Killing magnetic curves in ℍ3, Int. J. Geom. Methods Mod. Phys., 20 (14) (2023) 2450006.
  • [10] Adachi T., Kähler magnetic fields on a complex projective space, Proc. Japan Acad., 70 (1994) 12-13.
  • [11] Adachi T., Kähler Magnetic flow for a manifold of constant holomorphic sectional curvature, Tokyo J. Math., 18 (1995) 473-483.
  • [12] Adachi T., Kähler magnetic fields on Kähler manifolds of negative curvature, Differential Geom. Appl., 29 (2011) S2-S8.
  • [13] Kalinin, D.A., Trajectories of charged particles in Kähler magnetic fields, Rep. Math. Phys., 39(3) (1997) 299-309.
  • [14] Ateş O., Munteanu M. I., Periodic J-trajectories on R×S3, J. Geom. Phys., 133 (2018) 141-152.
  • [15] Inoguchi J., Lee J., J-trajectories in Vaisman manifolds, Differential Geom. Appl., 82(101882) (2022) 1-21.
  • [16] Inoguchi J., J-trajectories in Locally Conformal Kahler Manifolds with Parallel Anti Lee Field, International Electronic Journal of Geometry, 13(2) (2020) 30-44.
  • [17] Jleli M., Munteanu M.I., Magnetic curves on flat para-Kähler manifolds, Turkish Journal of Mathematics, 39(6) (2015) 963-969.
  • [18] Erjavec Z., Inoguchi J., Magnetic curves in ℍ3×ℝ, J. Korean Math. Soc., 58(6) (2021) 1501–1511.
  • [19] Yau S.T., Einstein manifolds with zero Ricci curvature, Surveys in differential geometry: essays on Einstein manifolds, Int. Press, Boston, MA, (1999) 1-14.
  • [20]Battista E., Esposito G., Geodesic motion in Euclidean Schwarzschild geometry, Eur. Phys. J. C, 82(1088) (2022) 1-13.
  • [21] Etesi G., Hausel T., Geometric interpretation of Schwarzschild instantons, J. Geom. Phys., 37 (1–2) (2001) 126-136.
  • [22] Rajan D., Complex spacetimes and the Newman–Janis trick, Master thesis, Victoria University of Wellington, School of Mathematics and Statistics, 2015.
  • [23]Dragomir S., Ornea L., Locally Conformal Kähler Geometry,1st ed. Birkhäuser Boston, (1998) 1–5.

Kähler Magnetic Curves in Conformally Euclidean Schwarzschild Space

Year 2024, , 147 - 152, 28.03.2024

Özgür Kelekçi

https://doi.org/10.17776/csj.1400543

Abstract

In this paper, we study the magnetic curves on a Kähler manifold which is conformally equivalent to Euclidean Schwarzschild space. We show that Euclidean Schwarzschild space is locally conformally Kähler and transform it into a Kähler space by applying a conformal factor coming from its Lee form. We solve Lorentz equation to find analytical expressions for magnetic curves which are compatible with the almost complex structure of the proposed Kähler manifold. We also calculate the energy of magnetic curves.

Keywords

Magnetic curve Lorentz equation Kähler magnetic fields Euclidean Schwarzschild metric

References

  • [1] Hinterleitner I., Mikes J., On F-planar mappings of spaces with affine connections, Note Mat., 27(1) (2007) 111–118.
  • [2] Cabrerizo J.L., Fernandez M., Gomez J., On the existence of almost contact structure and the contact magnetic field, Acta. Math. Hungar., 125 (2009) 191-199.
  • [3] Cabrerizo J.L., Fernandez M., Gomez J., The contact magnetic flow in 3D Sasakian manifolds, J. Phys. A: Math. Theor., 42(19) (2009) 195-201.
  • [4] Munteanu M. I., Nistor A.I., The classification of Killing magnetic curves in S2× R, J. Geom. Phys., 62(2) (2012) 170-182.
  • [5] Druţă-Romaniuc S.L., Inoguchi J., Munteanu M.I., Nistor A.I., Magnetic curves in Sasakian manifolds, J. Nonlinear Math. Phys., 22(3) (2015) 428–447.
  • [6] Druţă-Romaniuc S.L., Inoguchi J., Munteanu M.I., Nistor A.I., Magnetic curves in cosymplectic manifolds, Rep. Math. Phys., 78 (1) (2016) 33-48.
  • [7] Erjavec Z., Inoguchi, J., Magnetic curves in Sol3, J. Nonlinear Math. Phys., 25(2) (2018) 198-210.
  • [8] Inoguchi, J., Munteanu, M.I., Magnetic curves in the real special linear group, Adv. Theor. Math. Phys., 23 (8) (2019) 2161-2205.
  • [9] Kelekçi Ö., Dündar F.S., Ayar G., Classification of Killing magnetic curves in ℍ3, Int. J. Geom. Methods Mod. Phys., 20 (14) (2023) 2450006.
  • [10] Adachi T., Kähler magnetic fields on a complex projective space, Proc. Japan Acad., 70 (1994) 12-13.
  • [11] Adachi T., Kähler Magnetic flow for a manifold of constant holomorphic sectional curvature, Tokyo J. Math., 18 (1995) 473-483.
  • [12] Adachi T., Kähler magnetic fields on Kähler manifolds of negative curvature, Differential Geom. Appl., 29 (2011) S2-S8.
  • [13] Kalinin, D.A., Trajectories of charged particles in Kähler magnetic fields, Rep. Math. Phys., 39(3) (1997) 299-309.
  • [14] Ateş O., Munteanu M. I., Periodic J-trajectories on R×S3, J. Geom. Phys., 133 (2018) 141-152.
  • [15] Inoguchi J., Lee J., J-trajectories in Vaisman manifolds, Differential Geom. Appl., 82(101882) (2022) 1-21.
  • [16] Inoguchi J., J-trajectories in Locally Conformal Kahler Manifolds with Parallel Anti Lee Field, International Electronic Journal of Geometry, 13(2) (2020) 30-44.
  • [17] Jleli M., Munteanu M.I., Magnetic curves on flat para-Kähler manifolds, Turkish Journal of Mathematics, 39(6) (2015) 963-969.
  • [18] Erjavec Z., Inoguchi J., Magnetic curves in ℍ3×ℝ, J. Korean Math. Soc., 58(6) (2021) 1501–1511.
  • [19] Yau S.T., Einstein manifolds with zero Ricci curvature, Surveys in differential geometry: essays on Einstein manifolds, Int. Press, Boston, MA, (1999) 1-14.
  • [20]Battista E., Esposito G., Geodesic motion in Euclidean Schwarzschild geometry, Eur. Phys. J. C, 82(1088) (2022) 1-13.
  • [21] Etesi G., Hausel T., Geometric interpretation of Schwarzschild instantons, J. Geom. Phys., 37 (1–2) (2001) 126-136.
  • [22] Rajan D., Complex spacetimes and the Newman–Janis trick, Master thesis, Victoria University of Wellington, School of Mathematics and Statistics, 2015.
  • [23]Dragomir S., Ornea L., Locally Conformal Kähler Geometry,1st ed. Birkhäuser Boston, (1998) 1–5.
There are 23 citations in total.

Details

Primary Language English
Subjects Classical Physics (Other), Applied Mathematics (Other)
Journal Section Natural Sciences
Authors

Özgür Kelekçi 0000-0001-7617-0231

Publication Date March 28, 2024
Submission Date December 5, 2023
Acceptance Date March 4, 2024
Published in Issue Year 2024

Cite

APA Kelekçi, Ö. (2024). Kähler Magnetic Curves in Conformally Euclidean Schwarzschild Space. Cumhuriyet Science Journal, 45(1), 147-152. https://doi.org/10.17776/csj.1400543