Araştırma Makalesi
BibTex RIS Kaynak Göster

Yıl 2024, , 147 - 152, 28.03.2024

Özgür Kelekçi

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

Öz

Kaynakça

  • [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

Yıl 2024, , 147 - 152, 28.03.2024

Özgür Kelekçi

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

Öz

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.

Anahtar Kelimeler

Magnetic curve Lorentz equation Kähler magnetic fields Euclidean Schwarzschild metric

Kaynakça

  • [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.
Toplam 23 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Klasik Fizik (Diğer), Uygulamalı Matematik (Diğer)
Bölüm Natural Sciences
Yazarlar

Özgür Kelekçi 0000-0001-7617-0231

Yayımlanma Tarihi 28 Mart 2024
Gönderilme Tarihi 5 Aralık 2023
Kabul Tarihi 4 Mart 2024
Yayımlandığı Sayı Yıl 2024

Kaynak Göster

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