A study on magnetic curves in trans-Sasakian manifolds

[1]T. Adachi, Kahler magnetic fields on a complex projective space, Proceedings of the Japan Academy, Series A, Mathematical Sciences, 70(1), (1994) 12-13.Search in Google Scholar

[2]P. Baird, J.C. Wood, Harmonic morphisms between Riemannian manifolds London Mathematical Society Monographs. 29, Oxford Univ.Press. (2003).Search in Google Scholar

[3]M. Barros, A. Romero, J. L. Cabrerizo, M. Fernndez, The Gauss-Landau-Hall problem on Riemannian surfaces, J. Math. Phys., 46 (2005) 112905-112920.Search in Google Scholar

[4]Ş.N. Bozdağ, F.E. Erdoğan, f-Biharmonic and Bi-f-Harmonic Magnetic Curves in Three-Dimensional Normal Almost Paracontact Metric Manifolds, Int. Electronic Journal of Geometry, 14(2), (2021) 331-347.Search in Google Scholar

[5]J. Cabrerizo, M. Fernández, J. Gómez, On the existence of almost contact structure and the contact magnetic field, Acta Mathematica Hungarica 125(1-2), (2009) 191-199.Search in Google Scholar

[6]J. L. Cabrerizo, M. Fernández, J. S. Gómez, The contact magnetic flow in 3D Sasakian manifolds, J. Phys. A 42(19), (2009) 1-15.Search in Google Scholar

[7]C. Calin, M. Crasmareanu, Magnetic curves in three-dimensional quasi-para-Sasakian geometry, Mediterranean Journal of Mathematics, 13, (2016) 2087-2097.Search in Google Scholar

[8]G. Calvaruso, M.I. Munteanu, A. Perrone, Killing magnetic curves in three-dimensional almost paracontact manifolds, Journal of Mathematical Analysis and Applications 426(1), (2015) 423-439.Search in Google Scholar

[9]Y. J. Chiang, f-biharmonic maps between Riemannian manifolds. In Proc. of the Fourteenth Int. Conference on Geometry, Integrability and Quantization, (2013) 74-86.Search in Google Scholar

[10]D. Chinea, C. Gonzales, A classification of almost contact metric manifolds, Ann. Mat. Pura Appl., (4)156, (1990) 1536.Search in Google Scholar

[11]A. Comtet, On the Landau levels on the hyperbolic plane. Annals of Physics, 173(1), (1987) 185209.Search in Google Scholar

[12]N. Course, f-harmonic maps (Doctoral dissertation, Ph. D Thesis), (2004).Search in Google Scholar

[13]S. Deshmukh, Geometry of 3-dimensional trans-Sasakaian manifolds, An. Stiint. Univ. Al. I Cuza Iasi Mat, 63 (2016) 183-192.Search in Google Scholar

[14]S.L. Druta-Romaniuc, M.I. Munteanu, Magnetic curves corresponding to Killing magnetic fields in E³ , Journal of Mathematical Physics. 52(11), (2011) 1-14.Search in Google Scholar

[15]S.L. Druta-Romaniuc, M.I. Munteanu, Killing magnetic curves in a Minkowski 3-space, Nonlinear Analysis: Real World Applications. 14(1), (2013) 383-396.Search in Google Scholar

[16]S.L. Druta-Romaniuc, J. Inoguchi, M.I. Munteanu, A. I. Nistor, Magnetic curves in Sasakian manifolds, Jou. Nonlinear Math. Phy. 22(3), (2015) 428-447.Search in Google Scholar

[17]J. Eells, J.H. Sampson, Harmonic mappings of Riemannian manifolds, American Journal of Mathematics, 86, (1964) 109-160.Search in Google Scholar

[18]J. Eells, L. Lemaire, A report on harmonic maps. Bulletin of the London Mathematical Society, 10, (1978) 1-68.Search in Google Scholar

[19]A. Gray, L. M. Hervella, The sixteen classes of almost hermitian manifolds and their linear invariants, Ann. Mat. Pura Appl., (4)123, 1980 3558.Search in Google Scholar

[20]S. Jianguo, The equations and characteristics of the magnetic curves in the sphere space, Advances in Mathematical Physics, Article ID 7694306, (2019).Search in Google Scholar

[21]G.Y. Jiang, 2-Harmonic maps and their first and second variational formulas, Chinese Ann Math Ser-A, 7, (1986) 389-402.Search in Google Scholar

[22]W.J. Lu, On f-biharmonic maps and bi-f-harmonic maps between Riemannian manifolds, Science China Mathematics, 58, (2015) 1483-1498.Search in Google Scholar

[23]W.J. Lu, On f-biharmonic maps between Riemannian manifolds. arXiv:1305.5478 (2013).Search in Google Scholar

[24]J.C. Marrero, The local structure of trans-Sasakian manifolds, Ann. Mat. Pura Appl., 162 (1992) 7786.Search in Google Scholar

[25]M.I. Munteanu and A.I. Nistor, The classification of Killing magnetic curves in S² ×R, Journal of Geometry and Physics, 62(2), (2012) 170182.Search in Google Scholar

[26]Y.L. Ou, Some constructions of biharmonic maps and Chens conjecture on biharmonic hypersurfaces, Journal of Geometry and Physics, 62, (2012) 751762.Search in Google Scholar

[27]Y.L. Ou, On f-biharmonic maps and f-biharmonic submanifolds, Pacific Journal of Mathematics, 271(2), (2014) 461-477.Search in Google Scholar

[28]J. A. Oubina, New classes of almost contact metric structures, Publ. Math. Debrecen, 32, (1985) 187-193.Search in Google Scholar

[29]S.Y. Perktaş, A.M. Blaga, B.E. Acet, F.E. Erdoğan, Magnetic biharmonic curves on 3-dimensional normal almost paracontact metric manifolds, AIP Conference Proceedings, 020004,(2018).Search in Google Scholar

[30]S.Y. Perktaş, E. Kılıç, Biharmonic Maps between Doubly Warped Product Manifolds, Balkan Journal of Geometry and its Applications, 15(2), (2010) 159170.Search in Google Scholar

[31]S.Y. Perktaş, A.M. Blaga, F.E. Erdoğan, B.E. Acet, Bi-f-Harmonic Curves and Hypersurfaces, Filomat, 33(16), (2019) 5167-5180.Search in Google Scholar

[32]T. Sunada, Magnetic flows on a Riemann surface, Proceedings of the KAIST mathematics workshop, 8, (1993) 93108.Search in Google Scholar