Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
권호 표지
DOI QR코드

DOI QR Code

F-BIHARMONIC CURVES IN THREE-DIMENSIONAL GENERALIZED SYMMETRIC SPACES

  • YASMINE BAHOUS (Department of Mathematics, Laboratory of Pure and Applied Mathematics, University of Mostaganem (U.M.A.B.)) ;
  • LAKEHAL BELARBI (Department of Mathematics, Laboratory of Pure and Applied Mathematics, University of Mostaganem (U.M.A.B.)) ;
  • MANSOUR BELARBI (Department of Mathematics, Laboratory of Pure and Applied Mathematics, University of Mostaganem (U.M.A.B.)) ;
  • HICHEM ELHENDI (Department of Mathematics, University of Bechar)
  • Received : 2023.05.09
  • Accepted : 2023.09.16
  • Published : 2024.01.30
Download PDF
⟨ Previous Next ⟩

Abstract

In this work we give the necessary and sufficient conditions for f-biharmonic curves in three-dimensional generalized symmetric spaces.

Keywords

Acknowledgement

The authors would like to thank the Referees for all helpful comments and suggestions that have improved the quality of our initial manuscript. The authors were supported by The National Agency Scientific Research (DGRSDT).

References

  1. P. Baird, J.C. Wood, Harmonic morphisms between Riemannian manifolds, London Math. Soc. Monogr. (N.S.) 29, Oxford Univ. Press, 2003.
  2. C.L. Bejan, M. Benyounes, Harmonic φ Morphisms, Beitrge zur Algebra und Geometry 44 (2003), 309-321.
  3. L. Belarbi, On the Symmetries of Three-Dimensional Generalized Symmetric Spaces, Bull. Transilv. Univ. Brasov SER. III, 13 (2020), 451-462.
  4. L. Belarbi, M. Belarbi and H. Elhendi, Legendre Curves on Lorentzian Heisenberg Space, Bull. Transilv. Univ. Brasov SER. III, 13 (2020), 41-50.
  5. L. Belarbi and H. ElHendi, Harmonic and biharmonic maps between tangent bundles, Acta. Math. Univ. Comenianae 88 (2019), 187-199.
  6. L. Belarbi and H.Elhendi, Harmonic vector fields on gradient Sasaki metric, Afr. Mat. 34 (2023), 1-13.
  7. L. Belarbi and H. Zoubir, On translation surfaces with zero Gaussian curvature in Lorentzian Sol3 space, J. Appl. Math. Inform. 40 (2022), 831-842.
  8. N. Course, f-harmonic maps, New York J. Math. 13 (2007), 423-435.
  9. N. Course, f-harmonic maps. Ph.D thesis, University of Warwick, Coventry, CV4 7AL, UK, 2004.
  10. J. Cerny and O. Kowalski, Classification of generalized symmetric pseudo-Riemannian spaces of dimension n ≤ 4, Tensor, N.S. 38 (1980), 258-267.
  11. J.T. Cho, Ji-Eun Lee, Slant curves in contact pseudo-Hermitian 3-manifolds, Bull. Aust. Math.Soc. 78 (2008), 383-396. https://doi.org/10.1017/S0004972708000737
  12. R. Caddeo, S. Montaldo and C. Oniciuc, Biharmonic submanifolds of S3, Internat. J. Math. 12 (2001), 867-876. https://doi.org/10.1142/S0129167X01001027
  13. R. Caddeo, S. Montaldo and C. Oniciuc, Biharmonic submanifolds in spheres, Israel J. Math. 130 (2002), 109-123. https://doi.org/10.1007/BF02764073
  14. R. Caddeo, S. Montaldo and P. Piu, Biharmonic curves on a surface, Rend. Mat. Appl. 21 (2001), 143-157.
  15. R. Caddeo, S. Montaldo, C. Oniciuc and P. Piu, The classification of biharmonic curves of Cartan-Vranceanu 3-dimensional spaces, The 7th Int. Workshop on Dif. Geo. and its Appl., 2006, 121-131.
  16. R. Caddeo, C. Oniciuc, and P. Piu, Explicit formulas for non-geodesic biharmonic curves of the Heisenberg group, Rend. Sem. Mat. Univ. Politec. Torino. 62 (2004), 265-277.
  17. J. Eells, J.H. Sampson, Harmonic mappings of Riemannian manifolds, Amer. J. Math. 86 (1964), 109-160. https://doi.org/10.2307/2373037
  18. H. Elhendi and L. Belarbi, Deformed Diagonal Metrics on Tangent Bundle of Order Two and Harmonicity, Panamer. Math. J. 27 (2017), 90-106.
  19. H. Elhendi and L. Belarbi, On paraquaternionic submersions of tangent bundle of order two, Nonlinear Studies 25 (2018), 653-664.
  20. S. Guvenc, C. Ozgur, On the characterizations of f-biharmonic Legendre curves in Sasakian space forms, Filomat 31 (2017), 639-648. https://doi.org/10.2298/FIL1703639G
  21. J. Inoguchi, Biminimal submanifolds in contact 3-manifolds, Balkan J. Geom. Appl. 12 (2007), 56-67.
  22. G.Y. Jiang, 2-harmonic isometric immersions between Riemannian manifolds, Chinese Ann. Math. Ser. A 7 (1986), 130-144.
  23. G.Y. Jiang, Harmonic maps and their first and second variational formulas, Chinese Ann. Math. Ser. A. 7 (1986), 389-402.
  24. F. Karaca, C. Ozgur, On f-Biharmonic Curves, International Electronic Journal of Geometry 11 (2018), 18-27. https://doi.org/10.36890/iejg.545115
  25. O. Kowalski, Generalized symmetric spaces, Lectures Notes in Math., Springer-Verlag, Berlin, Heidelberg, New York, 1980.
  26. J.-E. Lee, Biharmonic spacelike curves in Lorentzian Heisenberg space, Commun. Korean Math. Soc. 33 (2018), 1309-1320.
  27. W.J. Lu, On f-biharmonic maps and bi-f-harmonic maps between Riemannian manifolds, Sci. China Math. B 58 (2015), 1483-1498. https://doi.org/10.1007/s11425-015-4997-1
  28. H. Mazouzi, H. El hendi and L. Belarbi, On the Generalized Bi-f-harmonic Map Equations on Singly Warped Product Manifolds, Comm. Appl. Nonlinear Anal. 25 (2018), 52-76.
  29. Ye-Lin Ou, On f-biharmonic maps and f-biharmonic submanifolds, Pacific J. Math. 271 (2014), 461-477. https://doi.org/10.2140/pjm.2014.271.461
  30. Ye-Lin Ou and Ze-Ping Wang, Linear biharmonic maps into Sol, Nil and Heisenberg spaces, Mediterr. J. Math. 5 (2008), 379-394. https://doi.org/10.1007/s00009-008-0157-y
  31. Ye-Lin Ou and Ze-Ping Wang, Biharmonic maps into sol and nil spaces, arXiv:math/0612329v1[math.DG]13 Dec 2006. 25 (2018), 52-76.
  32. S. Ouakkas, R. Nasri, and M. Djaa, On the f-harmonic and f-biharmonic maps, JP J. Geom. Topol. 10 (2010), 11-27.