The Complete Classification of Quarter-Symmetric Magnetic Curves in S-manifolds

Document Type : Research Paper

Author

Department of Mathematics, Balikesir University, Turkey

Abstract

In this paper, we consider $S$-manifolds endowed with a quarter-symmetric metric connection. We obtain the condition for a curve to be magnetic with respect to this connection. We show that quarter-symmetric magnetic curves are $\theta _{\alpha }-$slant curves of osculating order $r\leq 3$ with constant quarter-symmetric curvature functions. Finally, we give the classification theorem.

Keywords

References

[1] Adachi ,T., Curvature bound and trajectories for magnetic  elds on a Hadamard surface. Tsukuba J. Math. 20, 225{230, (1996).
[2] Blair, D. E., Geometry of manifolds with structural group U(n)  O(s), J. Di erential Geometry, 4, 155-167, (1970).
[3] Blair, D. E., Riemannian geometry of contact and symplectic manifolds, Second edition. Progress in Mathematics, 203. Birkhauser Boston, Inc., Boston, MA, (2010).
[4] Barros M., Romero, A., Cabrerizo, J. L., Fernandez, M., The Gauss-Landau-Hall problem on Riemannian surfaces. J. Math. Phys. 46, no. 11, 112905, 15 pp, (2005).
[5] Cabrerizo, J. L., Fernandez M. and Gomez, J. S., On the existence of almost contact structure and the contact magnetic  eld. Acta Math. Hungar. 125, 191-199, (2009).
[6] Comtet, A., On the Landau levels on the hyperbolic plane, Ann. Physics 173, 185-209, (1987).
[7] Druta-Romaniuc, S. L., Inoguchi, J., Munteanu, M. I., Nistor, A. I., Magnetic curves in Sasakian manifolds, Journal of Nonlinear Mathematical Physics, 22, 428-447, (2015).
[8] Golab, S., On Semi-symmetric and quarter-symmetric connections, Tensor, N.S. 29, 249-254, (1975).
[9] Gocmen, A., Quarter Symmetric Connections in S-manifolds, MSc Thesis, Supervisor: Prof. Dr. Aysel TURGUT VANLI, (2013).
[10] Guvenc, S., An Extended Family of Slant Curves in S-manifolds, Mathematical Sciences and Applications E-Notes 8 (1), 69-77, (2020).
[11] Guvenc, S., Ozgur, C., On slant curves in S-manifolds, Communications of the Korean Mathematical Society 33 (1), 293-303, (2018).
[12] Guvenc, S., Ozgur, C., On Pseudo-Hermitian Magnetic Curves in Sasakian Manifolds, Facta Universitatis, Series: Mathematics and Informatics 35 (5), 1291-1304, (2020).
[13] Jleli, M., Munteanu, M. I., Nistor, A. I., Magnetic trajectories in an almost contact metric manifold R2N+1, Results Math. 67, 125-134, (2015).
[14] Jordan, C., , Sur la theorie des courbes dans l'espace a n dimensions, C. R. Acad. Sci. Paris 79, 795{797 (1874).
[15] Ledger, A., Espace de Riemann symetriques generalises, C. R. Acad. Sci. Paris 264, 947-948, (1967).
[16] Ledger, A., Obata, M., Ane and Riemannian s-manifolds, J. Di erential Geometry 2, 451-459, (1968).
[17] Lee, J.-E., Pseudo-Hermitian magnetic curves in normal almost contact metric 3-manifolds, Communications of the Korean Mathematical Society, 35 (4), 1269-1281,(2020).
[18] Ozgur, C., Guvenc, S., On Biharmonic Legendre Curves in S-Space Forms, Turkish Journal of Mathematics 38 (3), 454-461, (2014).
[19] Tsagas, Gr., Ledger, A., Riemannian S-manifolds, J. Di erential Geometry 12, 333-343, (1977).
[20] Turgut Vanl, A., Semi-Symmetry Properties of S-Manifolds Admitting a Quarter-Symmetric Metric Connection, Hagia Sophia Journal of Geometry, Vol. 2, No. 2, 38-47,2020.
[21] Yano, K., Kon, M., Structures on Manifolds. Series in Pure Mathematics, 3. Singapore. World Scienti c Publishing Co. (1984).
Journal of Mahani Mathematical Research
Volume 12, Issue 1 - Serial Number 24
January 2023
Pages 151-160

Files

History

  • Receive Date: 25 April 2022
  • Revise Date: 17 June 2022
  • Accept Date: 03 July 2022

Share

How to cite

Statistics