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Journals / Konuralp Journal of Mathematics / 2026 / Volume: 14 Issue: 1

$ Q $-Frame Normal Parallel Curves in $ 3 $-Dimensional Euclidean Space

Mevlüt Canbirdi(Şeyh Edebali Üniversitesi Fen Fakültesi Matematik Bölümü)
Osman Zeki Okuyucu(Bilecik Şeyh Edebali Üniversitesi Fen Fakültesi)0000-0003-4379-0252
Pages
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Publication Date
2026-04-30
DOI
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AI Summary & Key Takeaways

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

Accordingly, the frame elements of the q -frame normal parallel curve for the projection vectors k = (1,0,0) , k = (0,1,0) and k = (0,0,1) are given separately.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this article, the parallel curve of a unit speed curve with respect to its quasi-frame in 3-dimensional Euclidean space is studied.
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Key Findings & Data:The definition of the q -frame parallel curve based on the quasi-normal vector at a constant distance from the unit speed curve is provided.
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Conclusion & Impact:Accordingly, the frame elements of the q -frame normal parallel curve for the projection vectors k = (1,0,0) , k = (0,1,0) and k = (0,0,1) are given separately.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:$q$-frame · $q$-frame normal parallel curves. · The quasi frame of the normal parallel curves

Abstract

In this article, the parallel curve of a unit speed curve with respect to its quasi-frame in 3-dimensional Euclidean space is studied. The definition of the q -frame parallel curve based on the quasi-normal vector at a constant distance from the unit speed curve is provided. Accordingly, the frame elements of the q -frame normal parallel curve for the projection vectors k = (1,0,0) , k = (0,1,0) and k = (0,0,1) are given separately.

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Cite This Article

Canbirdi, M., Okuyucu, O. Z. (2026). $ Q $-Frame Normal Parallel Curves in $ 3 $-Dimensional Euclidean Space. Konuralp Journal of Mathematics, Volume: 14 Issue: 1. https://ajindex.com/articles/1521443

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References (21)

  1. Gray, A., Modern Differential Geometry of Curves and Surfaces with Mathematica, CRC Press, Florida, 1998.
  2. Carmo, M., Differential Geometry of Curves and Surfaces, Instituto de Matematica Pura e Aplicada, Rio de Janeiro, Brazil, 1976.
  3. Hacısalihog˘lu, H. H., Diferansiyel Geometri 1. Cilt, Ankara U¨ niversitesi Fen Edebiyat Faku¨ltesi, 1998.
  4. Sabuncuo˘glu, A., Diferansiyel Geometri, 5. Basım, Nobel Yayınları, 2014.
  5. Yu¨ce, S., O¨ klid Uzayında Diferansiyel Geometri 5. Baskı, Pegem Akademi, 2020.
  6. Kaya, Y., K¨uc¸ ¨uk, A., Meleko˘glu, A., Diferansiyel Geometriye Giris¸, Dora Yayınları, 2015.
  7. Ersoy, S., Akyig˘it, M., Yıldız, O¨. G., Eg˘riler Teorisi, Nobel Yayınları 1. Basım, 2023.
  8. Dede, M., Ekici, C., G¨org¨ul¨u, A., Directional q-frame along a space curve, IJARCSSE, 5(12) (2015), 775-780.
  9. Erisir, T., Eren, K., Spinor representation of directional q-frame, Sigma J. Eng. Nat. Sci., 41(5) (2023), 1013-1018.
  10. Kalmuk, R., Bu¨yu¨kku¨tu¨k, S., O¨ ztu¨rk, G., Curves of constant ratio with quasi frame in E3, Tr. J. Nature Sci., Special Issue(1) (2024), 103-108.
  11. Elsharkawy, A., Tashkandy, Y., Emam, W., Cesarano, C., Elsharkawy, N., On some quasi-Curves in Galilean three-space, Axioms, 12 (2023), 823.
  12. Elsharkawy, A., Baizeed, H., Some integral curves according to quasi-frame in Euclidean 3-space, Scientic African, 27 (2025), e02583.
  13. Dede, M., Ekici, C., G¨uven, ˙I. A., Directional Bertrand Curves, GU J Sci., 31(1) (2018), 202-211.
  14. O¨ zen, KE., Tosun, M., On the resolution of the acceleration vector according to Bishop frame, Univ. J. Math. Appl., 4 (1) 2021, 26-32.
  15. Oruc¸, U., Turan, M., O¨ zkaldı Karakus¸, S., direction curves of vectorial moments with respect to an alternative frame in euclidean space, Commun. Adv. Math. Sci., 8 (4) 2025, 247-260.
  16. Aldossary, M. T., Gazwani, M. A., Motion of parallel curves and surfaces in Euclidean 3-space R3, Global Journal of Advanced Research on Classical and Modern Geometries, 9(1), (2020), 43-56.
  17. G¨uler, F., The quasi parallel curve of a space curve, Celal Bayar University Journal of Science, 18(2) (2022), 203-206.
  18. Sag˘ırog˘lu, Y., Ko¨se, G., Parallel curves based on normal vector, Sinop U¨ niversitesi Fen Bilimleri Dergisi, 9(1) (2024), 1-13.
  19. Dede, M., Ekici, C., Tozak, H., Directional tubular surfaces, International Journal of Algebra, 9(12) (2015), 527- 535.
  20. Ersoy, S., Akyig˘it, M., Yıldız, O¨. G., Eg˘riler Teorisi, Nobel Yayınları 1. Basım, 2023.
  21. Dede, M., Ekici, C., G¨org¨ul¨u, A., Directional q-frame along a space curve, IJARCSSE, 5(12) (2015), 775-780.