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Open Access ·Peer-reviewed·ISSN (Online): 2169-012X·ISSN (Print): 0972-0502

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Open Access Research Article

On generalization of biharmonic curves in a Walker 3-manifold

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pp. 1–9Vol. 29Issue 1January 2026DOI: 10.47974/JIM-2021XML
Received:
05 Dec 2023
Published Online:
27 Dec 2025
Article type:
Research Article
Language:
EN
Article no.:
JIM-2021
Pages:
1–9

Abstract

This paper examines f-biharmonic curves within a three-dimensional Walker manifold, focusing on their geometric properties. It derives explicit parametric equations for these curves and establishes the necessary and sufficient conditions for a curve to be f-biharmonic. In particular, we proved that when the function f remains constant, the f-biharmonic curve reduces to a non-geodesic biharmonic curve.

Keywords

Subject Classifications

53C2053C50

References

[1] M. Altunbas, on f-biharmonic curves in the three-dimensional Lorentzian Sasakian manifolds, HSJG, vol. 3, No. 2, pp. 24-30 (2021).
[2] B. O’Neill, Semi-riemannian geometry., Department of mathematics University of California Los Angeles, California (1983).
[3] M. Brozos-Vazquez, E. Garcia-Rio, P. Gilkey, S. Nikevic and R. Vazquez-Loenzo, The geometry ofWalker manifolds, Synthesis Lectures on Mathematics and Statistics, Morgan and Claypool Publishers, Williston, VT (2009).
[4] L. Du and J. Zhang, Classification of f-Biharmonic curves in Lorentz-Minkowski space, J. Math., Article ID 7529288 (2020).
[5] F. Karaca, C. Özgür, On f-biharmonic curves, International Electronic Journal of Geometry, vol. 11, No. 2, pp. 18-27 (2018).
[6] M. P. do Carmo, Differential Geometry of Curves and Surfaces, Prentice-Hall, Englewood Cliffs, NJ, USA (1976).
[7] J. Eells and J. H. Sampson, Harmonic mappings of Riemannian manifolds. American Journal of Mathematics, vol. 86, no. 1, pp. 109-160 (1964).
[8] M. Gningue, A. Ndiaye and R. Nkunzimana, Biharmonic Curves in a Strict Walker 3-Manifold. Int. J. Math. Math. Sci, Article ID 3855033 (2023). https://doi.org/10.1155/2022/3855033
[9] J. I. Inoguchi, Biharmonic curves in Minkowski 3-space, Int. J. Math. Math. Sci., vol. 2003, no. 21, pp. 1365-1368 (2003).
[10] W. J. Lu, On f-Bi-Harmonic maps between Riemannian manifolds, arXiv : 1305.5478v1 (2013).
[11] T. KŁorpinar, E. Turhan, Inextensible flows of biharmonic S-curves according to Sabban frame in Heisenberg group Heis3. Journal of Interdisciplinary Mathematics, Vol. 21, no. 1, pp. 17-27 (2018). https://doi.org/10.1080/09720502.2017.1390841
[12] A. Niang, A. Ndiaye, and A. S. Diallo, A classification of strict walker 3-manifold, Konuralp J. Math. vol. 9, no. 1, pp. 148-153 (2021).
[13] A. G. Walker, Canonical form for a Riemannian space with a parallel field of null planes, Quart. J. Math. Oxford, Vol. 1, no. 2, pp. 69-79 (1950).
[14] Y. L. Ou , On f-biharmonic maps and f-biharmonic manifolds, Pacific Journal of Mathematics., Vol. 271, no. 2, pp. 461-477 (2014).
[15] K. Derkaoui, F. Hathout, and H. M. Dida, “Slant curves and Legendre curves in three-dimensional Walker manifolds,” Asian-European Journal of Mathematics, no. 2350087, pp. 1–13(2023).

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