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Dergiler / Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics / 2026 / Volume: 75 Issue: 2

Generalized Elastic Line, Differentials of Maps Connected with CNLSE via Conformal Derivative and Magnetic Curves for Darboux Frame

Nevin Ertuğ Gürbüz(ESKISEHIR OSMANGAZI UNIVERSITY)0000-0003-3959-1779
Sayfa
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Yayın Tarihi
2026-06-30
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Finally, we present formulas for conformal differentials of maps associated with the CNLSE for the Darboux frame in $\mathbb{R}^{3}$.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:In this paper, we study generalized elastic lines via the intrinsic directional derivatives for the Darboux frame in $\mathbb{R}^{3}$.
📊
Temel Bulgular & Veri:Subsequently, we investigate the congruences of surfaces associated with the Darboux frame in $\mathbb{R}^{3}$.
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Sonuç & Katkı:Finally, we present formulas for conformal differentials of maps associated with the CNLSE for the Darboux frame in $\mathbb{R}^{3}$.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Darboux frame · generalized elastic line · anholonomic coordinates

Özet

In this paper, we study generalized elastic lines via the intrinsic directional derivatives for the Darboux frame in $\mathbb{R}^{3}$. Subsequently, we investigate the congruences of surfaces associated with the Darboux frame in $\mathbb{R}^{3}$. Furthermore, we establish the Darboux conformal derivative equations and conformal magnetic curves for the Darboux frame in $\mathbb{R}^{3}$. Finally, we present formulas for conformal differentials of maps associated with the CNLSE for the Darboux frame in $\mathbb{R}^{3}$.

Abstract

In this paper, we study generalized elastic lines via the intrinsic directional derivatives for the Darboux frame in $\mathbb{R}^{3}$. Subsequently, we investigate the congruences of surfaces associated with the Darboux frame in $\mathbb{R}^{3}$. Furthermore, we establish the Darboux conformal derivative equations and conformal magnetic curves for the Darboux frame in $\mathbb{R}^{3}$. Finally, we present formulas for conformal differentials of maps associated with the CNLSE for the Darboux frame in $\mathbb{R}^{3}$.

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Bu Makaleye Atıf Yap

Gürbüz, N. E. (2026). Generalized Elastic Line, Differentials of Maps Connected with CNLSE via Conformal Derivative and Magnetic Curves for Darboux Frame. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, Volume: 75 Issue: 2. https://doi.org/10.31801/cfsuasmas.1592170

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Kaynakça (49)

  1. Abdeljawad, T. (2015). On conformable fractional calculus. Journal of Computational and Applied Mathematics, 279:57–66.
  2. Adachi, T. (1994). Kahler magnetic on a complex projective space. Proceedings of the Japan Academy, Series A, Mathematical Sciences, 70:12–13.
  3. Arroyo, J., Barros, M., and Garay, O. (2004). Models of relativistic particle with curvature and torsion revisited. General Relativity and Gravitation, 36:1441–1451.
  4. Aydin, G., Gürbüz, N., Görgülü, A., and Çöken, A. C. (2015). Relaxed elastic lines of second kind in dual space. International Journal of Geometric Methods in Modern Physics, 12:1550016.
  5. Aydın, M. E., Bektaş, M., Ögrenmiş, A. O., and Yokuş, A. (2021). Differential geometry of curves in Euclidean 3-space with fractional order. International Electronic Journal of Geometry, 14:132–144.
  6. Balakrishnan, R. (1994). Space curve evolution, geometric phase and solitons. Theoretical and Mathematical Physics, 99:172–176.
  7. Barros, M., Cabrerizo, J. L., Fernández, M., and Romero, A. (2007). Magnetic vortex filament flows. Journal of Mathematical Physics, 48:082904.
  8. Barros, M. and Garay, O. (2012). Critical curves for the total normal curvature in surfaces of 3- dimensional space forms. Journal of Mathematical Analysis and Applications, 389:275–292.
  9. Cabrerizo, J. L., Fernandez, M., and Gomez, J. S. (2009). On the existence of almost contact structure and the contact magnetic field. Acta Mathematica Hungarica, 125:191–199.
  10. Capovilla, R., Chryssomalakos, C., and Guven, J. (2002). Hamiltonians for curves. Journal of Physics A: Mathematical and General, 35:6571–6587.
  11. Da Rios, L. S. (1906). On the motion of an unbounded fluid with a vortex filament of any shape. Rendiconti del Circolo Matematico di Palermo, 22.
  12. do Carmo, M. P. (1992). Riemannian Geometry. Birkhäuser, Boston.
  13. Druta-Romaniuc, S. L. and Munteanu, M. I. (2011). Magnetic curves corresponding to Killing magnetic fields in E3. Journal of Mathematical Physics, 52:113506.
  14. Ertuğ, N. G. (2018a). Öklidyen uzayda Darboux çatısına göre eğri evolüsyonunun üç sınıfına göre Hasimoto yüzeyleri. In Fen Bilimleri ve Matematik Alanında Akademik Çalışmalar. Gece Publishing.
  15. Ertuğ, N. G. (2018b). Three classes of non-lightlike curve evolution according to Darboux frame and geometric phase. International Journal of Geometric Methods in Modern Physics, 15:1850023.
  16. Ertuğ, N. G. (2021). The variation of electric field with respect to Darboux triad in Euclidean 3-space. Mathematical Combinatorics, 2:17–32.
  17. Ertuğ, N. G. (2022a). The change of electric field and relaxed elastic line via anholonomic coordinates with Darboux frame in $\mathbb{R}^{3}_{1}$. Optik, 270:170023.
  18. Ertuğ, N. G. (2022b). The null geometric phase along optical fiber for anholonomic coordinates. Optik, 258:168841.
  19. Ertuğ, N. G. (2023). The evolution of an electric field, Hasimoto surfaces and three differential formulas with the new frame in $\mathbb{R}^{3}_{1}$. Optik, 272:170217.
  20. Ertuğ, N. G. (2024). Geometric phase and Hasimoto-like maps via the anholonomic coordinates in Lorentzian 3-Lie group. Waves in Random and Complex Media.
  21. Ertuğ, N. G., Myrzakulov, R., and Myrzakulova, Z. (2022). Three anholonomy densities for three formulations with anholonomic coordinates with hybrid frame in $\mathbb{R}^{3}_{1}$. Optik, 261:169161.
  22. Ferrández, A., Guerrero, J., Javaloyes, M. A., and Lucas, P. (2006). Particles with curvature and torsion in three-dimensional pseudo-Riemannian space forms. Journal of Geometry and Physics, 56:1666–1687.
  23. Görgülü, A. and Ekici, C. (2010). Intrinsic equations for a generalized relaxed elastic line on an oriented surface. Hacettepe Journal of Mathematics and Statistics, 39:197–203.
  24. Görgülü, A. and Gürbüz, N. E. (2015). Generalized elastic line deformed on a nonnull surface by an external field in the 3-dimensional semi-Euclidean space. Ukrainian Mathematical Journal, 67:333–340.
  25. Gözütok, U., Coban, H. A., and Sagiroglu, Y. (2019). Frenet frame with respect to conformable derivative. Filomat, 33:1541–1550.
  26. Gürbüz, N. (2005). The differential formula of Hasimoto transformation in Minkowski space. Inter- national Journal of Mathematics and Mathematical Sciences, 16:2609–2616.
  27. Gürbüz, N. E. (2006). $p$-elastica in the 3-dimensional Lorentzian space forms. Turkish Journal of Mathematics, 30:33–41.
  28. Gürbüz, N. E. (2010). Particle with torsion in the Minkowski space $\mathbb{R}^{3}_{1}$. Advanced Studies in Theoretical Physics, 4:101–108.
  29. Gürbüz, N. E. (2013). Intrinsic formulation for elastic line deformed on a surface by an external field in the pseudo-Galilean space. Life Science Journal, 10:1348–1352.
  30. Gürbüz, N. E. (2015). Moving non-null curves according to Bishop frame in Minkowski 3-space. International Journal of Geometric Methods in Modern Physics, 12:1550052.
  31. Gürbüz, N. E. and Görgülü, A. (2000a). Intrinsic equations for a relaxed elastic line on an oriented surface in the Minkowski space $\mathbb{R}^{3}_{1}$. Hadronic Journal, 23:143–163.
  32. Gürbüz, N. E. and Görgülü, A. (2000b). Intrinsic equations for a relaxed elastic line on an oriented surface in the Minkowski space $\mathbb{R}^{n}_{1}$. Turkish Journal of Mathematics, 24:283–294.
  33. Gürbüz, N. E. and Görgülü, A. (2014). On dual r-elastic line. International Journal of Geometric Methods in Modern Physics, 11:1450079.
  34. Hasimoto, H. (1971). Motion of a vortex filament and its relation to elastica. Journal of the Physical Society of Japan, 31:293–294.
  35. Hasimoto, H. (1972). A soliton on a vortex filament. Journal of Fluid Mechanics, 51:477–485.
  36. Khalil, R., Al Horani, M., Yousef, A., and Sababheh, M. (2014). A new definition of fractional derivative. Journal of Computational and Applied Mathematics, 264:65–70.
  37. Körpinar, T., Körpinar, Z., and Özdemir, H. (2024). Conformable modeling of normalization and recursional electromagnetic fields of spacelike magnetic curves. Optical and Quantum Electronics, 56:834.
  38. Kuznetsov, Y. A. and Plyushchay, M. S. (1994). (2+1)-dimensional models of relativistic particles with curvature and torsion. Journal of Mathematical Physics, 35:2772–2784.
  39. Langer, J. and Perline, R. (1990). The Hasimoto transformation and integrable flows on curves. Applied Mathematics Letters, 3:61–64.
  40. Langer, J. and Singer, D. A. (1984). The total squared curvature of closed curves. Journal of Differential Geometry, 20:1–22.
  41. Manning, G. S. (1987). Relaxed elastic line on a curved surface. Quarterly of Applied Mathematics, 45:515–527.
  42. Marris, A. W. and Passman, S. L. (1969). Vector fields and flows on developable surfaces. Archive for Rational Mechanics and Analysis, 32:29–86.
  43. Nickerson, H. K. and Manning, G. S. (1988). Intrinsic equations for a relaxed elastic line on an oriented surface. Geometriae Dedicata, 27:127–136.
  44. Özdemir, Z., Gök, İ., Yaylı, Y., and Ekmekci, N. (2015). Notes on magnetic curves in 3d semi- Riemannian manifolds. Turkish Journal of Mathematics, 39:412–426.
  45. Plyushchay, M. S. (1991). The model of relativistic particle with torsion. Nuclear Physics B, 362:54–72.
  46. Ricca, R. L. (1996). The contributions of Da Rios and Levi-Civita to asymptotic potential theory and vortex filament dynamics. Fluid Dynamics Research, 18:245–268.
  47. Rogers, C. and Schief, W. K. (1998). Intrinsic geometry of the NLS equation and its auto-Bäcklund transformation. Studies in Applied Mathematics, 101:267–287.
  48. Singer, D. (2008). Lectures on elastic curves and rods. In AIP Conference Proceedings, volume 1002, Melville, New York. American Institute of Physics.
  49. Yajima, T., Oiwa, S., and Yamasaki, K. (2018). Geometry of curves with fractional-order tangent vector and Frenet–Serret formulas. Fractional Calculus and Applied Analysis, 21:1493–1505.