Timelike Bertrand Curves in Semi-Euclidean Space

Abstract

In this paper, it is proved that, no special timelike Frenet curve is a Bertrand curve in ${\mathbb{E}}_2^4$ and also, in ${\mathbb{E}}_{\nu }^{n+1}$ $(n\ge 3)$, such that the notion of Bertrand curve is definite only in ${\mathbb{E}}_1^2$ and ${\mathbb{E}}_1^3$. Therefore, a generalization of timelike Bertrand curve is defined and called as timelike (1,3)-Bertrand curve in ${\mathbb{E}}_2^4$. Moreover, the characterization of timelike (1,3)-Bertrand curve is given in ${\mathbb{E}}_2^4$.