f-Biharmonic and Bi-f-Harmonic Magnetic Curves in Three-Dimensional Normal Almost Paracontact Metric Manifolds

Yıl 2021, Cilt: 14 Sayı: 2, 331 - 347, 29.10.2021

Şerife Nur Bozdağ , Feyza Esra Erdoğan

Öz

In this paper, we study f-harmonic, f-biharmonic, bi-f-harmonic and f-biminimal non-null magnetic curves in three-dimensional normal almost paracontact metric manifolds. We determine necessary and sufficient conditions for these properties of a non-null magnetic curve. Besides, we obtain absence theorems.

Anahtar Kelimeler

Magnetic curves, normal almost paracontact metric manifolds, f-harmonic curves, f-biharmonic curves, bi-f-harmonic curves, f-biminimal curves

Kaynakça

• [1] Ara, M.: Geometry of f-harmonic maps. Kodai Mathematical Journal. 22, 243-263 (1999).
• [2] Baird, P., Wood, JC.: Harmonic morphisms between Riemannian manifolds. London Mathematical Society Monographs. 29, Oxford Univ.Press. (2003).
• [3] Caddeo, R.: Riemannian manifolds on which the distant function is biharmonic. Rendiconti del Seminario Matematico Universita Politecico Torino. 40, 93-101 (1982). https://doi.org/10.1515/math-2019-0112
• [4] Calin, C., Crasmareanu, M.: Magnetic curves in three-dimensional quasi-para-Sasakian geometry. Mediterranean Journal of Mathematics. 13, 2087-2097 (2016). https://doi.org/10.1007/s00009-015-0570-y
• [5] Calvaruso, G, Munteanu, M.I., Perrone, A.: Killing magnetic curves in three-dimensional almost paracontact manifolds. Journal of Mathematical Analysis and Applications 426(1), 423–439 (2015). https://doi.org/10.1016/j.jmaa.2015.01.057
• [6] Chang, S.Y.A., Wang, L., Yang, P.C.: A regularity theory of biharmonic maps. Communications on Pure and Applied Mathematics, 52, 1113-1137 (1999). https://doi.org/10.1002/(SICI)1097-0312(199909)52:91113::AID-CPA43.0.CO;2-7
• [7] Course, N.: f-harmonic maps, PhD Thesis, University of Warwick, Coventry, UK, (2004).
• [8] Dacko, P.: On almost para-cosymplectic manifolds. Tsukuba Journal of Mathematics. 28(1), 193-213 (2004).
• [9] Druta-Romaniuc, S.L., Munteanu, M.I.: Killing magnetic curves in a Minkowski 3-space. Nonlinear Analysis: RealWorld Applications. 14(1), 383–396 (2013). https://doi:10.1016/j.nonrwa.2012.07.002
• [10] Druta-Romaniuc, S.L., Munteanu, M.I.: Magnetic curves corresponding to Killing magnetic fields in E3 . Journal of Mathematical Physics. 52(11), 1–14 (2011). https://doi.org/10.1063/1.3659498
• [11] Eells, J., Sampson, J.H.: Harmonic mappings of Riemannian manifolds. American Journal of Mathematics. 86, 109–160 (1964).
• [12] Eells, J., Lemaire, L.: A report on harmonic maps. Bulletin of the London Mathematical Society. 10, 1–68 (1978).
• [13] Gürler, F., Özgür, C.: f-Biminimal immersions. Turkish Journal of Mathematics. 41, 564-575 (2017). https://doi:10.3906/mat-1508-23
• [14] Jianguo, S.: The equations and characteristics of the Magnetic Curves in the Sphere Space. Advances in Mathematical Physics. Article ID 7694306.(2019). https://doi.org/10.1155/2019/7694306
• [15] Kaneyuki S., Willams F.L.: Almost paracontact and paraHodge structures on manifolds. Nagoya Mathematical Journal. 99, 173-187 (1985).
• [16] Keleş, S., Perktaş, S.Y., Kılıç, E.: Biharmonic Curves in LP-Sasakian Manifolds. Bulletin of the Malaysian Mathematical Sciences Society. 33(2), 325–344 (2010). https://doi.org/10.1155/2019/7694306
• [17] Lu, W.J.: On f -biharmonic maps and bi-f-harmonic maps between Riemannian manifolds. Science China Mathematics. 58, 1483–1498 (2015).
• [18] Lu, W.J.: On f-biharmonic maps between Riemannian manifolds. Preprint arXiv:1305.5478 (2013).
• [19] Loubeau, E., Montaldo, S.: Biminimal immersions. Proceedings of the Edinburgh Mathematical Society, 51, 421-437 (2008). https://doi.org/10.1017/S0013091506000393
• [20] Montaldo, S., Oniciuc, C.: A short survey on biharmonic maps between Riemannian manifolds. Revista de la Union Matematica Argentina. 47(2), 1-22 (2006).
• [21] Ou, Y.L.: Some constructions of biharmonic maps and Chen’s conjecture on biharmonic hypersurfaces. Journal of Geometry and Physics, 62, 751–762 (2012). https://doi.org/10.1016/j.geomphys.2011.12.014
• [22] Ou, Y.L.: On f-biharmonic maps and f-biharmonic submanifolds. Pacific Journal of Mathematics. 271(2), 461–477 (2014).
• [23] Ouakkas, S., Nasri, R., Djaa, M.: On the f-harmonic and f-biharmonic maps. JP Journal of Geometry and Topology. 10, 11-27 (2010).
• [24] Perktaş, S.Y., Blaga, A.M., Acet, B.E., Erdoğan F.E.:Magnetic biharmonic curves on 3-dimensional normal almost paracontact metric manifolds. AIP Conference Proceedings. 020004,(2018). https://doi.org/10.1063/1.5047877
• [25] Perktaş, S.Y., Blaga, A.M., Erdoğan, F.E., Acet, B.E.: Bi-f-Harmonic Curves and Hypersurfaces. Filomat. 33(16), 5167-5180 (2019). https://doi.org/10.2298/FIL1916167P
• [26] Perktaş, S.Y., Kılıç, E.: Biharmonic Maps between Doubly Warped Product Manifolds. Balkan Journal of Geometry and its Applications. 15(2), 159–170 (2010).
• [27] Roth, J., Upadhyay, A.: f-biharmonic and bi-f-harmonic submanifolds of generalized space forms. Preprint arXiv. 1609.08599 (2016).
• [28] Sario, L., Nakai, M., Wang, C., Chung, L.: Classification theory of Riemannian manifolds, Harmonic, quasiharmonic and biharmonic function. Lecture Notes in Mathematic 605, Springer-Verlag, Berlin-New York, (1977).
• [29] Strzelecki, P.: On biharmonic maps and their generalizations. Calculus of Variations and Partial Differential Equations. 18, 401-432 (2003). https://doi: 10.1007/s100970200043.6.
• [30] Wang, C.: Remarks on biharmonic maps into spheres. Calculus of Variations and Partial Differential Equations. 21, 221-242 (2004). https://doi.org/10.1007/s00526-003-0252-7
• [31] Welyczko, J.: Slant curves in 3-dimensional normal almost paracontact metric manifolds. Mediterranean Journal of Mathematics. 11(3), 965-978 (2014). https://doi:10.1007/s00009-013-0361-20378-620X/14/030965-14
• [32] Welyczko, J.: On Legendre curves in 3-dimensional normal almost paracontact metric manifolds. Results in Mathematics. 54(34), 377-387 (2009).
• [33] Zamkovoy, S.: Canonical connection on paracontact manifolds. Annals of Global Analysis and Geometry. 36, 37-60 (2009) https://doi.org/10.1007/s10455-008-9147-3
• [34] Zhao, C.L., Lu, W.J.: Bi-f-harmonic map equations on singly warped product manifolds. Applied Mathematics-A Journal of Chinese Universities. 30(1), 111–126 (2015) https://doi:10.1007/s11766-015-3258-y