Demet Demir, Kazım İlarslan

DOI Number
First page
Last page


In this paper, we generalize the notion of Bertrand curve in Euclidean 3-space analogously as in Minkowski 3-space. According to this generalization, the Bertrand curve conditions of a given space curve are obtained and the relations between Frenet vectors and curvature functions are revealed. A curve that meets the given condition is constructed as an example.


Bertrand curve, Euclidean 3-space, Frenet vectors, curvature functions.

Full Text:



H. Balgetir, M. Bekta¸s and M. Ergüt, Bertrand curves for non-null curves in 3-dimensional Lorentzian space, Hadronic J. 27 (2004), no. 2, 229-236.

J. M. Bertrand, Mémoire sur la théorie des courbes á double courbure, Comptes Rendus, 36, (1850).

N. Ekmekci and K. ·Ilarslan, On Bertrand curves and their characterization, Di¤er. Geom. Dyn. Syst. 3 (2001), no. 2, 17-24.

S. Honda and M. Takahashi, Bertrand and Mannheim curves of framed curves in the 3- dimensional Euclidean space, Turk. J. Math., (2020) 44, 883-899.

D. H. Jin, Null Bertrand curves in a Lorentz manifold, J. Korea Soc. Math. Educ. Ser. B Pure Appl. Math. 15 (2008), no. 3, 209-215.

S. Özkaldi Karakus, K. ·Ilarslan and Y. Yayl¬, A new approach for characterization of curve couples in Euclidean 3-space, Honam Mathematical J. 36(2014), no.1, 113-129.

W. Kuhnel, Di¤erential geometry: curves-surfaces-manifolds, Braunschweig, Wiesbaden, (1999).

H. Matsuda and S. Yorozu, Notes on Bertrand curves, Yokohama Math. J. 50 (2003), no. 1-2, 41-58.

L. R. Pears, Bertrand curves in Riemannian space, J. London Math. Soc. Volumes 1-10, Number 2, 180-183 , July 1935.

A. Uçum, K. ·Ilarslan and S. Özkald¬Karaku¸s, Curve couples and spacelike Frenet planes in Minkowski 3-space, Honam Mathematical J. 36 (2014), No. 3, 475-492.

A. Uçum, O. Keçilio¼glu and K. ·Ilarslan, Generalized Bertrand curves with spacelike (1; 3)- normal plane in Minkowski space-time, Turk. J. Math. 40 (2016), 487-505.

B. Saint Venant, Mémoire sur les lignes courbes non planes, Journal de l'Ecole Polytechnique, vol. 18, pp.1-76, 1845.

C. Zhang and D. Pei, Generalized Bertrand curves in Minkowski 3-space, Mathematics, (2020), Vol.8, 2199

DOI: https://doi.org/10.22190/FUMI221215013D


  • There are currently no refbacks.

© University of Niš | Created on November, 2013
ISSN 0352-9665 (Print)
ISSN 2406-047X (Online)