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Journals / Fundamentals of Contemporary Mathematical Sciences / 2026 / Volume: 1 Issue: 1

On Biharmonic and Biminimal Curves in 3-dimensional f-Kenmotsu Manifolds

Selcen Yüksel Perktaş(ADIYAMAN ÜNİVERSİTESİ)0000-0002-8848-0621
Bilal Eftal Acet(ADIYAMAN UNIVERSITY)0000-0002-0190-3741
Seddik Ouakkas(University of Saida,)0000-0002-2485-3169
Pages
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Publication Date
2020-01-31
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

We give some related characterizations in case such curves are Legendre curves.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In the present paper, we study biharmonicity and biminimality of the curves in 3-dimensional f-Kenmotsu manifolds.
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Key Findings & Data:We investigate necessary and sufficient conditions for a slant curve in a 3-dimensional f-Kenmotsu manifold to be biharmonic and biminimal, respectively.
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Conclusion & Impact:We give some related characterizations in case such curves are Legendre curves.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Biharmonic curves · Biminimal Curves · f-Kenmotsu Manifolds

Abstract

In the present paper, we study biharmonicity and biminimality of the curves in 3-dimensional f-Kenmotsu manifolds. We investigate necessary and sufficient conditions for a slant curve in a 3-dimensional f-Kenmotsu manifold to be biharmonic and biminimal, respectively. We give some related characterizations in case such curves are Legendre curves.

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Cite This Article

Perktaş, S. Y., Acet, B. E., Ouakkas, S. (2020). On Biharmonic and Biminimal Curves in 3-dimensional f-Kenmotsu Manifolds. Fundamentals of Contemporary Mathematical Sciences, Volume: 1 Issue: 1. https://ajindex.com/articles/1486335

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References (14)

  1. Călin C., Crasmareanu M., Munteanu M.I., Slant curves in three-dimensional f -Kenmotsu manifolds, J. Math. Anal. Appl., 394, 400-407, 2012.
  2. Blair D.E., Contact Manifolds in Riemannian Geometry, Lect. Notes Math., 509, 1976.
  3. Olszak Z., Locally conformal almost cosymplectic manifolds, Colloq. Math., 57, 73–87, 1989.
  4. Janssens D., Vanhecke L., Almost contact structures and curvature tensors, Kodai Math. J., 4(1), 1–27, 1981.
  5. Kenmotsu K., A class of almost contact Riemannian manifolds, Tohoku Math. J., 24, 93–103, 1972.
  6. Mangione V., Harmonic maps and stability on f-Kenmotsu manifolds, Int. J. Math. Math. Sci., 7, Article ID798317, 2008.
  7. Olszak Z., Rosca R., Normal locally conformal almost cosymplectic manifolds, Publ. Math. Debrecen, 39, 315–323, 1991.
  8. Cho J.T., Inoguchi J.-I., Lee J.-E., On slant curves in Sasakian 3-manifolds, Bull. Austral. Math. Soc., 74(3), 359–367, 2006.
  9. Baikoussis Ch., Blair D.E., On Legendre curves in contact 3-manifolds, Geom. Dedicata, 49(2), 135–142, 1994.
  10. Eells J., Sampson J.H., Harmonic mappings of Riemannian manifolds, Amer. J. Math., 86, 109–160, 1964.
  11. Jiang G.Y., 2-harmonic isometric immersions between Riemannian manifolds, Chinese Ann. Math. Ser. A, 7, 130–144, 1986.
  12. Jiang G.Y., 2-harmonic maps and their first and second variational formulas, Chinese Ann. Math. Ser. A, 7, 389–402, 1986.
  13. Loubeau E., Montaldo S., Biminimal immersions, Proc. Edinb. Math. Soc., 51, 421–437, 2008.
  14. Montaldo S., Oniciuc C., A short survey on biharmonic maps between Riemannian manifolds, Rev. De La Union Math. Argentina, 47(2), 1-22, 2006.