Variational equations and Killing magnetic trajectories on timelike surfaces in semi-Riemannian manifolds

(Bozkurt) Özdemir, Zehra; ŞAHİN, Kübra

doi:10.15672/hujms.967923

Variational equations and Killing magnetic trajectories on timelike surfaces in semi-Riemannian manifolds

Kübra Şahin, (Amasya Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bölümü, Amasya, Türkiye)

Zehra Özdemir (Amasya Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bölümü, Amasya, Türkiye)

Hacettepe Journal of Mathematics and Statistics

0 0

Yıl: 2022 Cilt: 51 Sayı: 4 Sayfa Aralığı: 1058 - 1071 Metin Dili: İngilizce DOI: 10.15672/hujms.967923 İndeks Tarihi: 11-04-2023

Variational equations and Killing magnetic trajectories on timelike surfaces in semi-Riemannian manifolds

Öz:

In this article, Darboux frame variations for timelike surfaces in semi-Riemannian mani- folds are discussed. In addition, the Killing equations are examined by using the Darboux frame curvature variations. Then, magnetic trajectories are generated by means of the variational vector fields. Furthermore, parametric representations of all magnetic trajec- tories on the de Sitter space S21 are presented. Moreover, various examples of magnetic trajectories are given in order to illustrate the theoretical results.

Anahtar Kelime: vector fields magnetic flows ordinary differential equations special curves motion of a rigid body with a fixed point variational methods

Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık

[1] M. Barros, J.L. Cabrerizo, M. Fernández and A. Romero, Magnetic vortex flament flows, J. Math. Phys. 48, 1-27, 2007.
[2] M. Barros, A. Ferrandez, P. Lucas and M.A. Merono, General helices in the 3- dimensional Lorentzian space forms, Rocky. Mt. J. Math. 32, 373-388, 2001.
[3] M. Barros, A. Romero, J.L. Cabrerizo and M. Fernández, The Gauss Landau Hall problem on Riemannian surfaces. J. Math. Phys.46, 112905, 2005.
[4] Z. Bozkurt, I. Gök, Y. Yaylı and F.N. Ekmekci, A new approach for magnetic curves in 3D Riemannian manifolds, J. Math. Phys. 55, 053501, 2014.
[5] J.L. Cabrerizo, Magnetic fields in 2D and 3D sphere, J. Nonlinear. Math. Phys. 20, 440-450, 2013.
[6] H.S.M. Coxeter, A geometrical background for de Sitter’s world, Am. Math. Mon. (Math. Assoc. Am.) 50 (4), 217-228 (JSTOR 2303924), 1943.
[7] W. de Sitter, On the relativity of inertia remarks concerning Einstein’s latesthypoth- esis, Proc. Kon. Ned. Acad. Wet. 19, 1217-1225, 1917.
[8] S.L. Druta-Romaniuc and M.I. Munteanu, Magnetic Curves corresponding to Killing magnetic fields in E3, J. Math. Phys. 52, 113506, 2011.
[9] S.L. Druta-Romaniuc and M.I. Munteanu, Killing magnetic curves in a Minkowski 3-space, Nonlinear. Anal. Real. World. Appl. 14, 383-396, 2013.
[10] N. Gurbuz, p-Elastica in the 3-Dimensional Lorentzian Space Forms, Turkish J. Math. 30, 33-41, 2006.
[11] R. Lopez, Differential Geometry of Curves and Surfaces in Lorentz-Minkowski Space. Int. Electronic. J. Geom. 7 (1), 44-107, 2014.
[12] B. O’Neill, Semi-Riemannian geometry with applications to relativity, Academic press, New York, 1983.
[13] Z. Özdemir, Pseudo Null Curve Variations for Bishop Frame in 3D semi-Riemannian Manifold, Int. J. Geom. Methods and Modern Phys. 16 (3), 1950043, 2019.
[14] Z. Özdemir, I. Gok, Y. Yaylı and F.N. Ekmekci, Notes on Magnetic Curves in 3D semi-Riemannian Manifolds. Turkish J. Math. 39, 412-426, 2015.
[15] Z. Özdemir, Null Cartan curve variations in 3D semi-Riemannian manifold, Hacettepe J. Math. Stat. 50 (2), 351-360, 2021.
[16] T. Sunada, Magnetic flows on a Riemann surface, In Proceedings of the KAIST Mathematics Workshop:Analysis and Geometry, Taejeon, Korea, 3-6, 1993.
[17] H.H. Ugurlu, H. Kocayigit, The Frenet and Darboux Instantaneous Rotain Vectors of Curves on Time-like Surfaces, Math. Comput. Appl. 1 (2), 133-141, 1996.

APA	ŞAHİN K, (Bozkurt) Özdemir Z (2022). Variational equations and Killing magnetic trajectories on timelike surfaces in semi-Riemannian manifolds. , 1058 - 1071. 10.15672/hujms.967923
Chicago	ŞAHİN Kübra,(Bozkurt) Özdemir Zehra Variational equations and Killing magnetic trajectories on timelike surfaces in semi-Riemannian manifolds. (2022): 1058 - 1071. 10.15672/hujms.967923
MLA	ŞAHİN Kübra,(Bozkurt) Özdemir Zehra Variational equations and Killing magnetic trajectories on timelike surfaces in semi-Riemannian manifolds. , 2022, ss.1058 - 1071. 10.15672/hujms.967923
AMA	ŞAHİN K,(Bozkurt) Özdemir Z Variational equations and Killing magnetic trajectories on timelike surfaces in semi-Riemannian manifolds. . 2022; 1058 - 1071. 10.15672/hujms.967923
Vancouver	ŞAHİN K,(Bozkurt) Özdemir Z Variational equations and Killing magnetic trajectories on timelike surfaces in semi-Riemannian manifolds. . 2022; 1058 - 1071. 10.15672/hujms.967923
IEEE	ŞAHİN K,(Bozkurt) Özdemir Z "Variational equations and Killing magnetic trajectories on timelike surfaces in semi-Riemannian manifolds." , ss.1058 - 1071, 2022. 10.15672/hujms.967923
ISNAD	ŞAHİN, Kübra - (Bozkurt) Özdemir, Zehra. "Variational equations and Killing magnetic trajectories on timelike surfaces in semi-Riemannian manifolds". (2022), 1058-1071. https://doi.org/10.15672/hujms.967923

APA	ŞAHİN K, (Bozkurt) Özdemir Z (2022). Variational equations and Killing magnetic trajectories on timelike surfaces in semi-Riemannian manifolds. Hacettepe Journal of Mathematics and Statistics, 51(4), 1058 - 1071. 10.15672/hujms.967923
Chicago	ŞAHİN Kübra,(Bozkurt) Özdemir Zehra Variational equations and Killing magnetic trajectories on timelike surfaces in semi-Riemannian manifolds. Hacettepe Journal of Mathematics and Statistics 51, no.4 (2022): 1058 - 1071. 10.15672/hujms.967923
MLA	ŞAHİN Kübra,(Bozkurt) Özdemir Zehra Variational equations and Killing magnetic trajectories on timelike surfaces in semi-Riemannian manifolds. Hacettepe Journal of Mathematics and Statistics, vol.51, no.4, 2022, ss.1058 - 1071. 10.15672/hujms.967923
AMA	ŞAHİN K,(Bozkurt) Özdemir Z Variational equations and Killing magnetic trajectories on timelike surfaces in semi-Riemannian manifolds. Hacettepe Journal of Mathematics and Statistics. 2022; 51(4): 1058 - 1071. 10.15672/hujms.967923
Vancouver	ŞAHİN K,(Bozkurt) Özdemir Z Variational equations and Killing magnetic trajectories on timelike surfaces in semi-Riemannian manifolds. Hacettepe Journal of Mathematics and Statistics. 2022; 51(4): 1058 - 1071. 10.15672/hujms.967923
IEEE	ŞAHİN K,(Bozkurt) Özdemir Z "Variational equations and Killing magnetic trajectories on timelike surfaces in semi-Riemannian manifolds." Hacettepe Journal of Mathematics and Statistics, 51, ss.1058 - 1071, 2022. 10.15672/hujms.967923
ISNAD	ŞAHİN, Kübra - (Bozkurt) Özdemir, Zehra. "Variational equations and Killing magnetic trajectories on timelike surfaces in semi-Riemannian manifolds". Hacettepe Journal of Mathematics and Statistics 51/4 (2022), 1058-1071. https://doi.org/10.15672/hujms.967923