Timelike Bertrand Curves in Semi-Euclidean Space

Details Timelike Bertrand Curves in Semi-Euclidean Space Timelike Bertrand Curves in Semi-Euclidean Space

2010-03-05

arxiv.org/abs/1003.1220v1

Mathematics

Differential Geometry

Scientific paper

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 $\mathbb{E}_2^4$.

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