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Dergiler / Hagia Sophia Journal of Geometry / 2026 / Cilt: 7 Sayı: 1

Focal Surfaces Connected with VFF for Type 1-PAF in $\mathbb{E}{^{3}}$

Esin Şahin(ESKİŞEHİR OSMANGAZİ ÜNİVERSİTESİ, FEN-EDEBİYAT FAKÜLTESİ)0000-0001-8169-6465
Şerife Nevin Gürbüz(ESKISEHIR OSMANGAZI UNIVERSITY)0000-0003-3959-1779
Sayfa
1–14
Yayın Tarihi
2025-06-30
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Finaly, we provide examples related to focal surfaces generated by vortex filament flow surfaces for three classes according Type 1-PAF in Euclidean 3-space $\mathbb{E}{^{3}}$.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:In this paper, we obtain vortex filament flow (VFF) surfaces for three classes according to Type 1-PAF in Euclidean 3-space $\mathbb{E}{^{3}}$.
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Temel Bulgular & Veri:Additionally, we obtain the first and second fundamental forms, Gauss and mean curvatures of focal surfaces generated by vortex filament flow surfaces in Euclidean 3-space $\mathbb{E}{^{3}}$.
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Sonuç & Katkı:Finaly, we provide examples related to focal surfaces generated by vortex filament flow surfaces for three classes according Type 1-PAF in Euclidean 3-space $\mathbb{E}{^{3}}$.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:VFF · Type 1-PAF · Euclidean space

Özet

In this paper, we obtain vortex filament flow (VFF) surfaces for three classes according to Type 1-PAF in Euclidean 3-space $\mathbb{E}{^{3}}$. Additionally, we obtain the first and second fundamental forms, Gauss and mean curvatures of focal surfaces generated by vortex filament flow surfaces in Euclidean 3-space $\mathbb{E}{^{3}}$. Furthermore , we present focal surfaces generated by vortex filament flow for three classes according Type 1-PAF in Euclidean 3-space $\mathbb{E}{^{3}}$. Finaly, we provide examples related to focal surfaces generated by vortex filament flow surfaces for three classes according Type 1-PAF in Euclidean 3-space $\mathbb{E}{^{3}}$.

Abstract

In this paper, we obtain vortex filament flow (VFF) surfaces for three classes according to Type 1-PAF in Euclidean 3-space $\mathbb{E}{^{3}}$. Additionally, we obtain the first and second fundamental forms, Gauss and mean curvatures of focal surfaces generated by vortex filament flow surfaces in Euclidean 3-space $\mathbb{E}{^{3}}$. Furthermore , we present focal surfaces generated by vortex filament flow for three classes according Type 1-PAF in Euclidean 3-space $\mathbb{E}{^{3}}$. Finaly, we provide examples related to focal surfaces generated by vortex filament flow surfaces for three classes according Type 1-PAF in Euclidean 3-space $\mathbb{E}{^{3}}$.

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Bu Makaleye Atıf Yap

Şahin, E., Gürbüz, Ş. N. (2025). Focal Surfaces Connected with VFF for Type 1-PAF in $\mathbb{E}{^{3}}$. Hagia Sophia Journal of Geometry, Cilt: 7 Sayı: 1, 1–14. https://ajindex.com/articles/1490424

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Kaynakça (18)

  1. Özen, K. E., & Tosun, M. (2021). A new moving frame for trajectories with non-vanishing angular momentum. Journal of Mathematical Sciences and Modelling, 4(1), 7–18.
  2. Özen, K. E., Tosun, M., & Avcı, K. (2022). Type 2-positional adapted frame and its application to Tzitzeica and Smarandache curves. Karatekin University Journal of Science, 1(1), 42–53.
  3. Solouma, E. M. (2021). Characterization of Smarandache trajectory curves of constant mass point particles as they move along the trajectory curve via PAF. Bulletin of Mathematical Analysis and Applications, 13(4), 14–30.
  4. Gürbüz, N. E. (2022). The evolution an electric field with respect to the type 1-PAF and the PAFORS frames in R^3_1. Optik, 250(1), 168285.
  5. Gürbüz, N. E., & Yoon, D. W. (2024). The evolution of the electric field along optical fiber with respect to the type-2 and 3 PAFs in Minkowski 3-space. Tamkang Journal of Mathematics, 55(2), 113–128.
  6. Hasimoto, H. (1971). Motion of a vortex filament and its relation to elastica. J. Phys. Soc. Jpn., 31, 293–294.
  7. Hasimoto, H. (1972). A soliton on a vortex filament. J. Fluid. Mech. 51 (3), 477–485.
  8. Abdel-All, N. H., Hussien, R., & Taha, Y. (2012). Hasimoto surfaces. Life Science Journal, 9(3), 556–560.
  9. Lamb Jr, G. L. (1977). Solitons on moving space curves. Journal of Mathematical Physics, 18(8), 1654–1661.
  10. Lakshmanan, M. (1977). Continuum spin system as an exactly solvable dynamical system. Phys. Lett. A. 61(1), 53–54.
  11. Hagen, H., Hahmann, S., & Schreiber, T. (1995). Visualization and computation of curvature behaviour freeform curves and surfaces. Computer-Aided Design, 27 (7), 545–552.
  12. Hagen, H., Müller, H., & Nielson, G. M. (1993). Focus on scientific visualization. SpringerVerlag, Berlin Heidelberg, 252–258.
  13. Hagen, H., & Hahmann, S. (1993). Generalized focal surfaces: a new method for surface interrogation. IEEE Proceedings Visualization, 70–76.
  14. Honda. S., & Takahashi, M. (2020). Evolutes and focal surfaces of framed immersions in the Euclidean space. Proceedings of the Royal Society of Edinburgh Section A:Mathematics, 150 (1), 497–516.
  15. Güler, F. (2022). The focal surfaces of offset surface. Optik, 271, 170053.
  16. Al-Dayel, I., Solouma, E., & Khan, M. (2022). On geometry of focal surfaces due to B-Darboux and type-2 Bishop frames in Euclidean 3-space. AIMS Mathematics, 7, 13454–13468.
  17. Da Rios, L. S. (1906). Sul moto d’un liquido indefinito con un filetto vorticoso di forma qualunque. Rend. Circ. Matem. Palermo, 22 (1), 117–135.
  18. Şahin, E. (2023). Focal surfaces according to positional adapted frames (in Turkish). Master’s Thesis, Eskişehir Osmangazi University, Eskişehir.