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Annals of the Alexandru Ioan Cuza University - Mathematics

The Journal of "Alexandru Ioan Cuza" University from Iasi

Editor-in-Chief: Oniciuc, Cezar

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Generalized Null Bertrand Curves In Minkowski Space-Time

Ferdag Kahraman Aksoyak / Ismail Gok / Kazim Ilarslan
Published Online: 2014-11-24 | DOI: https://doi.org/10.2478/aicu-2013-0031


Çöken and ÇIFTCI proved that a null Cartan curve in Minkowski space-time E41 is a null Bertrand curve if and only if k2 is nonzero constant and k3 is zero. That is, the null curve with non-zero curvature k2 is not a Bertrand curve in Minkowski space-time E41.

So, in this paper we defined a new type of Bertrand curve in Minkowski space-time E41 for a null curve with non-zero curvature k3 by using the similar idea of generalized Bertrand curve given by Matsuda and Yorozu and we called it a null (1, 3)-Bertrand curve. Also, we proved that if a null curve with non-zero curvatures in Minkowski space-time E41 is a null (1, 3)-Bertrand curve then it is a null helix. We give an example of such curves.

Keywords: Minkowski space-time; null curve; Frenet vectors; Bertrand curves

MSC: 53C50; 53B30


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About the article

Received: 2011-11-24

Revised: 2012-10-23

Accepted: 2012-12-13

Published Online: 2014-11-24

Citation Information: Annals of the Alexandru Ioan Cuza University - Mathematics, Volume 60, Issue 2, Pages 489–502, ISSN (Online) 1221-8421, DOI: https://doi.org/10.2478/aicu-2013-0031.

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© 2014 Ferdag Kahraman Aksoyak et. al.. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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