- Turkish Journal of Mathematics
- Vol: 40 Issue: 3
- Generalized Bertrand Curves with Spacelike $\left(1,3\right) $-Normal Plane in Minkowski Space-Time
Generalized Bertrand Curves with Spacelike $\left(1,3\right) $-Normal Plane in Minkowski Space-Time
Authors : Ali Uçum, Osman Keçilioğlu, Kazim Ilarslan
Pages : 487-505
View : 8 | Download : 4
Publication Date : 9999-12-31
Article Type : Makaleler
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.Keywords : Bertrand curve, Minkowski space-time, Frenet planes