SavedAdd your journal

Journals / International Electronic Journal of Geometry / 2026 / Volume: 18 Issue: 1

Unveiling $\: f-$Biharmonic $\: \theta _{\alpha }-$Slant Curves in $\: \mathcal{S}-$Space Forms

Şaban Güvenç(BALIKESİR ÜNİVERSİTESİ, FEN-EDEBİYAT FAKÜLTESİ, MATEMATİK BÖLÜMÜ)0000-0001-6254-4693
Pages
—
Publication Date
2025-04-24
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

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

Finally, we present an example to support our findings.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we firstly provide a concise overview of $\mathcal{S}-$manifolds, $f$-biharmonicity and $\theta _{\alpha }$-slant curves.
📊
Key Findings & Data:We then derive a key equation and analyze it in detail to establish the necessary and sufficient conditions for $\theta _{\alpha }$-slant curves to be $f$-biharmonic.
💡
Conclusion & Impact:Finally, we present an example to support our findings.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:$\theta _{\alpha }-$slant curve · $f$-biharmonic curve · Frenet curve

Abstract

In this paper, we firstly provide a concise overview of $\mathcal{S}-$manifolds, $f$-biharmonicity and $\theta _{\alpha }$-slant curves. We then derive a key equation and analyze it in detail to establish the necessary and sufficient conditions for $\theta _{\alpha }$-slant curves to be $f$-biharmonic. Finally, we present an example to support our findings.

🔖

Cite This Article

Güvenç, Ş. (2025). Unveiling $\: f-$Biharmonic $\: \theta _{\alpha }-$Slant Curves in $\: \mathcal{S}-$Space Forms. International Electronic Journal of Geometry, Volume: 18 Issue: 1. https://ajindex.com/articles/1410939

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (20)

  1. Baikoussis, C., Blair, D. E.: On Legendre curves in contact 3-manifolds. Geom. Dedicata. 49, 135-142 (1994).
  2. Blair, D. E.: Geometry of manifolds with structural group U(n) × O(s). J. Differential Geometry. 4, 155-167 (1970).
  3. Blair, D. E.: Riemannian geometry of contact and symplectic manifolds, Second edition. Progress in Mathematics, 203. Birkhäuser Boston, Inc., Boston, MA (2010).
  4. Cabrerizo, J. L., Fernandez, L. M., Fernandez, M.: The curvature of submanifolds of an S-space form. Acta Math. Hungar. 62, 373-383 (1993).
  5. Chen, B.Y.: A report on submanifolds of finite type. Soochow J. Math. 22, 117-337 (1996).
  6. Cho, J. T., Inoguchi, J., Lee, J. E.: On slant curves in Sasakian 3-manifolds. Bull. Austral. Math. Soc. 74, 359-367 (2006).
  7. Eells, Jr. J., Lemaire, L.: Selected topics in harmonic maps. Amer. Math. Soc., Providence, R.I. (1983).
  8. Eells, Jr. J., Sampson, J. H.: Harmonic mappings of Riemannian manifolds. Amer. J. Math. 86, 109-160 (1964).
  9. Fetcu, D., Oniciuc, C.: Explicit formulas for biharmonic submanifolds in Sasakian space forms. Pacific J. Math. 240, 85-107 (2009).
  10. Güvenç, Ş., Özgür, C.: On slant curves in S-manifolds. Commun. Korean Math. Soc. 33(1), 293-303 (2018).
  11. Güvenç, Ş., Özgür, C.: C-parallel and C-proper Slant Curves of S-manifolds. Filomat 33(19), 6305-6313 (2019).
  12. Güvenç, Ş.: A Note on f-biharmonic Legendre Curves in S-space forms. International Electronic Journal of Geometry. 12(2), 260-267 (2019).
  13. Güvenç, Ş.: An Extended Family of Slant Curves in S-manifolds. Mathematical Sciences and Applications E-Notes. 8(1), 69-77 (2020).
  14. Hasegawa, I., Okuyama, Y., Abe, T.: On p-th Sasakian manifolds. J. Hokkaido Univ. Ed. Sect. II A. 37(1), 1-16 (1986).
  15. Jiang, G. Y.: 2-harmonic maps and their first and second variational formulas. Chinese Ann. Math. Ser. A. 7, 389-402 (1986).
  16. Kim, J. S., Dwivedi, M. K., Tripathi, M. M.: Ricci curvature of integral submanifolds of an S-space form. Bull. Korean Math. Soc. 44, 395-406 (2007).
  17. Nakagawa, H.: On framed f-manifolds. Kodai Math. Sem. Rep. 18, 293-306 (1966).
  18. Ou, Y. L.: On f-biharmonic maps and f-biharmonic submanifolds. Pacific Journal of Mathematics. 271(2), 461-477.
  19. Özgür, C., Güvenç, Ş.: On biharmonic Legendre curves in S-space forms. Turkish J. Math. 38(3), 454-461 (2014).
  20. Yano, K., Kon, M.: Structures on Manifolds. Series in Pure Mathematics. 3. World Scientific Publishing Co., Singapore (1984).