Journals / International Electronic Journal of Geometry / 2025 / Volume: 18 Issue: 2

Biharmonic Curves in Solvable Lie Group

Ji-Eun Lee(Chonnam National University)0000-0003-0698-9596
Pages
—
Publication Date
2025-10-19
🏛️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)

In particular, we find biharmonic almost Legendre curves in the solvable Lie group $G(c_1,c_2)$ with Lorentzian metric.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we study biharmonic curves in the solvable Lie group $G(c_1,c_2)$ with Lorentzian metric.
📊
Key Findings & Data:In this paper, we study biharmonic curves in the solvable Lie group $G(c_1,c_2)$ with Lorentzian metric.
💡
Conclusion & Impact:In particular, we find biharmonic almost Legendre curves in the solvable Lie group $G(c_1,c_2)$ with Lorentzian metric.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Almost Legendre curve · biharmonic curve · para-$\beta$-Kenmotau manifold

Abstract

In this paper, we study biharmonic curves in the solvable Lie group $G(c_1,c_2)$ with Lorentzian metric. In particular, we find biharmonic almost Legendre curves in the solvable Lie group $G(c_1,c_2)$ with Lorentzian metric.

🔖

Cite This Article

Lee, J. (2025). Biharmonic Curves in Solvable Lie Group. International Electronic Journal of Geometry, Volume: 18 Issue: 2. https://doi.org/10.36890/iejg.1660936

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (21)

  1. Chen, B. Y., Ishikawa, S.: Biharmonic surfaces in pseudo-Euclidean spaces. Mem. Fac. Sci. Kyushu Univ. Ser. A 45(2), 323–347 (1991).
  2. Cho, J.T., Inoguchi, J., Lee, J.-E.: Biharmonic curves in 3-dimensional Sasakian space form. Ann. Math. Pura Appl. 186, 685-701 (2007).
  3. Hawking, S.W., Ellis, G. F. R.: The large scale structure of space-time. Cambridge Monographs on Mathematical Physics 1. London: Cambridge University Press, 1973.
  4. Inoguchi, J.: Submanifolds with harmonic mean curvature vector field in contact 3-manifolds. Coll. Math. 100, 163-179 (2004).
  5. Inoguchi, J.: Minimal surfaces in 3-dimensional solvable Lie groups. Chinese Ann. Math. B. 24, 73-84 (2003).
  6. Inoguchi, J.: Minimal surfaces in 3-dimensional solvable Lie groups II. Bull. Austral. Math. Soc. 73, 365-374 (2006).
  7. Inoguchi, J.: Biharmonic curves in Minkowki 3-space. Int. J. Math. Math. Sci. 2003(21), 1365-1368 (2003).
  8. Inoguchi, J., Lee, S.: A Weierstrass representation for minimal surfaces in Sol. Proc. Amer. Math. Soc. 136, 2209-2216 (2008).
  9. Inoguchi, J., Lee, J. -E.: Slant curves in 3-dimensional almost contact metric geometry. Int. Electron. J. Geom. 8(2), 106–146 (2015).
  10. Lee, J. -E.: Biharmonic spacelike curves in Lorentzian Heigenberg space. Commun. Korean Math. Soc., 33(4), 1309–1320 (2018).
  11. Lee, J. -E.: Biharmonic curves in 3-dimensional Lorentzian Sasakian space forms. Commun. Korean Math. Soc., 35(3), 967–977 (2020).
  12. Lee, J. -E.: Pointwise slant curves in pseudo-Hermitian geometry,.Mediterr. J. math. 19, Article number 130 (2022).
  13. Sasahara, T.: Biharmonic submanifolds in normalflat Lorentz 3-space forms. Bull. Aust. Math. Soc. 85, 422–432 (2012).
  14. Tricerri, F., Vanhecke, L.: Homogeneous Structures on Riemannian Manifolds. Lecture Notes Series, London Math. Soc. 52, Cambridge Univ. Press (1983).
  15. Wełyczko, J.: Slant curves in 3-dimensional normal almost paracontact metric manifolds. Mediterr. J. math. 11, 965–978 (2014).
  16. Wełyczko, J.: On Legendre curves in 3-dimensional normal almost paracontact metric manifolds. Result. Math. 54, 377-387 (2009).
  17. Chen, B. Y., Ishikawa, S.: Biharmonic surfaces in pseudo-Euclidean spaces. Mem. Fac. Sci. Kyushu Univ. Ser. A 45(2), 323–347 (1991).
  18. Cho, J.T., Inoguchi, J., Lee, J.-E.: Biharmonic curves in 3-dimensional Sasakian space form. Ann. Math. Pura Appl. 186, 685-701 (2007).
  19. Hawking, S.W., Ellis, G. F. R.: The large scale structure of space-time. Cambridge Monographs on Mathematical Physics 1. London: Cambridge University Press, 1973.
  20. Lee, J. -E.: Biharmonic spacelike curves in Lorentzian Heigenberg space. Commun. Korean Math. Soc., 33(4), 1309–1320 (2018).
  21. Lee, J. -E.: Biharmonic curves in 3-dimensional Lorentzian Sasakian space forms. Commun. Korean Math. Soc., 35(3), 967–977 (2020).