Bertrand Curves in Minkowski Spacetime: A New Approach

Osman Keçilioğlu; Kazım İlarslan; Münevver Kübra Uçar

doi:10.31801/cfsuasmas.1788973

Bertrand Curves in Minkowski Spacetime: A New Approach

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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References

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Details

Primary Language

English

Subjects

Algebraic and Differential Geometry

Journal Section

Research Article

Authors

Osman Keçilioğlu
0000-0002-5149-5221
Türkiye

Kazım İlarslan ^*
0000-0003-1708-280X
Türkiye

Münevver Kübra Uçar
0009-0003-8896-8998
Türkiye

Publication Date

September 26, 2026

Submission Date

September 24, 2025

Acceptance Date

March 11, 2026

Published in Issue

Year 2026 Volume: 75 Number: 3

DOI

https://doi.org/10.31801/cfsuasmas.1788973

IZ

https://izlik.org/JA68EP54CN

Cite

RIS / Bibtex

APA

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, 75(3), 487-506. https://doi.org/10.31801/cfsuasmas.1788973

AMA

1.Keçilioğlu O, İlarslan K, Uçar MK. Bertrand Curves in Minkowski Spacetime: A New Approach. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2026;75(3):487-506. doi:10.31801/cfsuasmas.1788973

Chicago

Keçilioğlu, Osman, Kazım İlarslan, and Münevver Kübra Uçar. 2026. “Bertrand Curves in Minkowski Spacetime: A New Approach”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 75 (3): 487-506. https://doi.org/10.31801/cfsuasmas.1788973.

EndNote

Keçilioğlu O, İlarslan K, Uçar MK (September 1, 2026) Bertrand Curves in Minkowski Spacetime: A New Approach. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 75 3 487–506.

IEEE

[1]O. Keçilioğlu, K. İlarslan, and M. K. Uçar, “Bertrand Curves in Minkowski Spacetime: A New Approach”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 75, no. 3, pp. 487–506, Sept. 2026, doi: 10.31801/cfsuasmas.1788973.

ISNAD

Keçilioğlu, Osman - İlarslan, Kazım - Uçar, Münevver Kübra. “Bertrand Curves in Minkowski Spacetime: A New Approach”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 75/3 (September 1, 2026): 487-506. https://doi.org/10.31801/cfsuasmas.1788973.

JAMA

1.Keçilioğlu O, İlarslan K, Uçar MK. Bertrand Curves in Minkowski Spacetime: A New Approach. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2026;75:487–506.

MLA

Keçilioğlu, Osman, et al. “Bertrand Curves in Minkowski Spacetime: A New Approach”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 75, no. 3, Sept. 2026, pp. 487-06, doi:10.31801/cfsuasmas.1788973.

Vancouver

1.Osman Keçilioğlu, Kazım İlarslan, Münevver Kübra Uçar. Bertrand Curves in Minkowski Spacetime: A New Approach. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2026 Sep. 1;75(3):487-506. doi:10.31801/cfsuasmas.1788973