Generalized Bertrand Curves with Spacelike $\left(1,3\right) $-Normal Plane in Minkowski Space-Time

Authors

ALİ UÇUM
OSMAN KEÇİLİOĞLU
KAZIM İLARSLAN

Abstract

In this paper, we reconsider the $(1,3)$-Bertrand curves with respect to the casual characters of a $\left( 1,3\right) $-normal plane that is a plane spanned by the principal normal and the second binormal vector fields of the given curve. Here, we restrict our investigation of $(1,3)$-Bertrand curves to the spacelike $\left( 1,3\right) $-normal plane in Minkowski space-time. We obtain the necessary and sufficient conditions for the curves with spacelike $\left( 1,3\right) $-normal plane to be $(1,3)$-Bertrand curves and we give the related examples for these curves.

DOI

10.3906/mat-1503-12

Keywords

Bertrand curve, Minkowski space-time, Frenet planes

First Page

487

Last Page

505

Recommended Citation

UÇUM, ALİ; KEÇİLİOĞLU, OSMAN; and İLARSLAN, KAZIM (2016) "Generalized Bertrand Curves with Spacelike $\left(1,3\right) $-Normal Plane in Minkowski Space-Time," Turkish Journal of Mathematics: Vol. 40: No. 3, Article 2. https://doi.org/10.3906/mat-1503-12
Available at: https://journals.tubitak.gov.tr/math/vol40/iss3/2