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Dergiler / Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics / 2026 / Volume: 75 Issue: 3

Bertrand Curves in Minkowski Spacetime: A New Approach

Osman Keçilioğlu(KIRIKKALE UNIVERSITYFaculty of Engineering and Natural Sciences, Department of Mathematics)0000-0002-5149-5221
Kazım İlarslan(KIRIKKALE UNIVERSITY)0000-0003-1708-280X
Münevver Kübra Uçar(Kırıkkale University, Faculty of Engineering and Natural Sciences, Department of Mathematics)0009-0003-8896-8998
Sayfa
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Yayın Tarihi
2026-09-26
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

A number of examples are presented to demonstrate the theoretical results.

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Amaç & Hipotez:In this study, we establish the existence conditions of non-null Bertrand curve pairs in Minkowski spacetime that preserve the classical definition of Bertrand curves, namely curve pairs with parallel principal normal vectors, where both the curves and their Frenet vectors are non-null.
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Temel Bulgular & Veri:Furthermore, the existence of Combescure-related curves, which form a subclass of Bertrand curves, is demonstrated as a consequence of the results.
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Sonuç & Katkı:A number of examples are presented to demonstrate the theoretical results.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Bertand curves · Minkowski spacetime · non-null curves

Abstract

In this study, we establish the existence conditions of non-null Bertrand curve pairs in Minkowski spacetime that preserve the classical definition of Bertrand curves, namely curve pairs with parallel principal normal vectors, where both the curves and their Frenet vectors are non-null. The corresponding Bertrand mate curves are explicitly constructed. All obtained results are examined with respect to every possible causal character of the curves and their Frenet vectors. Furthermore, the existence of Combescure-related curves, which form a subclass of Bertrand curves, is demonstrated as a consequence of the results. A number of examples are presented to demonstrate the theoretical results.

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Bu Makaleye Atıf Yap

Keçilioğlu, O., İlarslan, K., Uçar, M. K. (2026). Bertrand Curves in Minkowski Spacetime: A New Approach. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, Volume: 75 Issue: 3. https://doi.org/10.31801/cfsuasmas.1788973

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Kaynakça (24)

  1. Balgetir, H., Bektaş, M., and Inoguchi, J. (2004). Null Bertrand curves in Minkowski 3-space and their characterizations. Note di Matematica, 23(1):7–13.
  2. Bertrand, J. M. (1850). Mémoire sur la théorie des courbes à double courbure. Comptes Rendus, 15:332–350.
  3. Camcı, Ç., Uçum, A., and İlarslan, K. (2020). A new approach to Bertrand curves in Euclidean 3-space. Journal of Geometry, 111(49).
  4. Camcı, Ç., Uçum, A., and İlarslan, K. (2021). Space curves related by a transformation of Combescure. Journal of Dynamical Systems and Geometric Theories, 19(2):271–287.
  5. Cheng, Y.-M. and Lin, C.-C. (2009). On the generalized Bertrand curves in Euclidean 𝑛-space. Note di Matematica, 29(2):33–39.
  6. Demir, D. and İlarslan, K. (2023). On generalized Bertrand curves in Euclidean 3-space. Facta Universitatis, Series: Mathematics and Informatics, 38(1):199–208.
  7. Ersoy, S. and Inalcık, A. (2014). Generalized spacelike Bertrand curves in Minkowski 5-space. Quaestiones Mathematicae, 37(1):19–29.
  8. Gök, I., Nurkan, S. K., and İlarslan, K. (2014). On pseudo null Bertrand curves in Minkowski space-time. Kyungpook Mathematical Journal, 54(4):685–697.
  9. Kahraman, F., Gök, I., and İlarslan, K. (2014). Generalized null Bertrand curves in Minkowski space-time. Analele Stiintifice Ale Universitatii Al I Cuza Din Iasi Matematica, 60(2):489–502.
  10. Kühnel, W. (1999). Differential Geometry: Curves–Surfaces–Manifolds. Vieweg, Braunschweig/Wiesbaden.
  11. Li, Y., Keçilioğlu, O., and İlarslan, K. (2025). Generalized Bertrand curve pairs in Euclidean four-dimensional space. Axioms, 14(4).
  12. Li, Y., Uçum, A., İlarslan, K., and Camcı, Ç. (2022). A new class of Bertrand curves in Euclidean 4-space. Symmetry, 14(6):1191.
  13. López, R. (2014). Differential geometry of curves and surfaces in Lorentz–Minkowski space. International Electronic Journal of Geometry, 7(1):44–107.
  14. Matsuda, H. and Yorozu, S. (2003). Notes on Bertrand curves. Yokohama Mathematical Journal, 50(1–2):41–58.
  15. O’Neill, B. (1983). Semi-Riemannian Geometry with Applications to Relativity. Academic Press, New York, NY, USA.
  16. Papaioannou, S. G. and Kiritsis, D. (1985). An application of Bertrand curves and surfaces to CAD/CAM. Computer-Aided Design, 17(8):348–352.
  17. Pears, L. R. (1935). Bertrand curves in Riemannian space. Journal of the London Mathematical Society, s1-10(2):180–183.
  18. Ravani, B. and Ku, T. S. (1991). Bertrand offsets of ruled and developable surfaces. Computer-Aided Design, 23(2):145–152.
  19. Saint-Venant, B. (1845). Mémoire sur les lignes courbes non planes. Journal de l’École Royale Polytechnique, 18:1–76.
  20. Schief, W. K. (2003). On the integrability of Bertrand curves and Razzaboni surfaces. Journal of Geometry and Physics, 45(1–2):130–150.
  21. Sun, J. and Zhao, Y. (2021). The geometrical characterizations of the Bertrand curves of the null curves in semi-Euclidean 4-space. Mathematics, 9(24):3294.
  22. Uçum, A., Keçilioğlu, O., and İlarslan, K. (2015). Generalized Bertrand curves with timelike $(1, 3)$- normal plane in Minkowski space-time. Kuwait Journal of Science, 42(3):10–27.
  23. Uçum, A., Keçilioğlu, O., and İlarslan, K. (2016). Generalized Bertrand curves with spacelike $(1, 3)$- normal plane in Minkowski space-time. Turkish Journal of Mathematics, 40(3):487–505.
  24. Zhang, C. and Pei, D. (2020). Generalized Bertrand curves in Minkowski 3-space. Mathematics, 8:2199.