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Journals / Bitlis Eren Üniversitesi Fen Bilimleri Dergisi / 2026 / Volume: 13 Issue: 2

On Equiform Rectifying, Normal and Osculating Curves in Minkowski Space-Time

Özgür Boyacıoğlu Kalkan(AFYON KOCATEPE ÜNİVERSİTESİ, AFYON MESLEK YÜKSEKOKULU)0000-0003-1665-233X
Pages
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Publication Date
2024-06-29
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AI Summary & Key Takeaways

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

We obtain the relationship between the curvatures for these curves to be congruent to a rectifying, normal and second kind osculating curve according to equiform geometry in Minkowski space-time.

📌 3 Key Takeaways

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Objective & Hypothesis:This paper deals with the equiform rectifying, normal and second kind osculating curves in Minkowski space-time .
📊
Key Findings & Data:We reveal necessary and sufficient conditions for a curve to be a rectifying, normal and second kind osculating curve according to equiform geometry in Minkowski space-time .
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Conclusion & Impact:We obtain the relationship between the curvatures for these curves to be congruent to a rectifying, normal and second kind osculating curve according to equiform geometry in Minkowski space-time.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Equiform Frenet frame · Rectifying curves · Normal curves

Abstract

This paper deals with the equiform rectifying, normal and second kind osculating curves in Minkowski space-time . We reveal necessary and sufficient conditions for a curve to be a rectifying, normal and second kind osculating curve according to equiform geometry in Minkowski space-time . We obtain the relationship between the curvatures for these curves to be congruent to a rectifying, normal and second kind osculating curve according to equiform geometry in Minkowski space-time.

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Cite This Article

Kalkan, Ö. B. (2024). On Equiform Rectifying, Normal and Osculating Curves in Minkowski Space-Time. Bitlis Eren Üniversitesi Fen Bilimleri Dergisi, Volume: 13 Issue: 2. https://doi.org/10.17798/bitlisfen.1426092

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References (21)

  1. A. T. Ali and M. Önder, “Some characterizations of spacelike rectifying curves in the Minkowski space-time”, Glob J Sci Front Res Math Decision Sci, vol. 12, no. 1, pp. 57-64, 2012.
  2. B. Y. Chen, “When does the position vector of a space curve always lie in its rectifying plane?”, Amer. Math. Monthly, vol. 110, pp. 147-152, 2003.
  3. B. Y. Chen and F. Dillen, “Rectifying curves as centrodes and extremal curves”, Bull. Inst. Math. Academia Sinica, vol. 2, pp. 77-90, 2005.
  4. B. O’Neill, “Semi-Riemannian geometry with applications to relativity”, Academic Press, London: 1983.
  5. H.S. Abdel-Aziz, M.K. Khalifa Saad, and A.A. Abdel-Salam, “Equiform Differential Geometry of Curves in Minkowski Space-Time”, 2015, arXiv:1501.02283v1 [math DG] January.
  6. J. Walrave, “Curves and surfaces in Minkowski space”, Ph.D. dissertation, Leuven University,1995.
  7. K. İlarslan and E. Nešovic, “Some characterizations of rectifying curves in the Euclidean space ”, Turkish. J. Math., vol. 32, no. 1, pp. 21-30, 2008.
  8. K. İlarslan, E. Nešovic, and M. Petrovic-Torgasev, “Some characterizations of rectifying curves in the Minkowski 3-space”, Novi Sad J. Math., vol. 33, no. 2, pp. 23-32, 2003.
  9. K. İlarslan and E. Nešovic, “Some characterizations of null, pseudo null and partially null rectifying curves in Minkowski space-time”, Taiwanese J. Math., vol. 12, no. 5, pp. 1035-1044, 2008.
  10. K. İlarslan, “Spacelike normal curves in Minkowski space ”, Turkish J. Math., vol. 29, no. 1, 53-63, 2005.
  11. K. İlarslan and E. Nešovic, “Timelike and null normal curves in Minkowski space ”, Indian J. Pure Appl. Math., vol. 35, no. 7, 881-888, 2004.
  12. K. İlarslan and E. Nešovic, “Spacelike and timelike normal curves in Minkowski space-time”, Publ. Inst. Math. (Belgrad) (N.S.), vol. 85, no. 99, pp. 111-118, 2009.
  13. K. İlarslan and E. Nešovic, “Some characterizations of osculating curves in the Euclidean spaces”, Demonstratio Mathematica, vol. 16, pp. 931-939, 2008.
  14. K. İlarslan and E. Nešovic, “The first kind and the second kind osculating curves in Minkowski space-time”, Compt. Rend. Acad. Bulg. Sci., vol. 62, no. 6, pp. 677-686, 2009.
  15. K. İlarslan and E. Nešovic, “Some characterizations of null osculating curves in the Minkowski space-time”, Proceedings of the Estonian Academy of Sciences, vol. 6, no. 1, pp. 1-8, 2012.
  16. K. İlarslan, N. Kılıç, and H. Altın Erdem, “Osculating curves in 4-dimensional semi-Euclidean space with index 2”, Open Mathematics, vol. 15, pp. 562-567, 2017.
  17. R. Lopez, “Differential geometry of curves and surfaces in Lorentz-Minkowski space”, Int. Electron. J. Geom., vol. 3, pp. 67-101, 2010.
  18. S. Yılmaz and M. Turgut, “On the Differential Geometry of the curves in Minkowski space-time”, Int. J. Contemp. Math. Sci., vol. 3, no. 7, pp. 1343-1349, 2008.
  19. M. Elzawy and S. Mosa, “Equiform rectifying curves in Galilean space ”, Scientific African, vol 22, e01931, 2023.
  20. M. Fakharany, A. El-Abed, M. Elzawy and S. Mosa, “On the geometry of equiform normal curves in the Galilean space ”, Inf. Sci. Lett., vol. 11, no. 5, pp. 1711-1715, 2022.
  21. D. W. Yoon, J. W. Lee and C. W Lee, “Osculating curves in the Galilean 4-space”, International Journal of Pure and Applied Mathematics, vol. 100, no. 4, pp. 497-506, 2015.