Turkish Journal of Mathematics
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, A, KEÇİLİOĞLU, O, & İLARSLAN, K (2016). Generalized Bertrand Curves with Spacelike $\left(1,3\right) $-Normal Plane in Minkowski Space-Time. Turkish Journal of Mathematics 40 (3): 487-505. https://doi.org/10.3906/mat-1503-12
