Journal of the
Korean Mathematical Society JKMS

We consider a curve $\alpha=\alpha(s)$ in Minkowski 3-space $\boldsymbol E_1^3$ and denote by $\{\boldsymbol T,\boldsymbol N,\boldsymbol B\}$ the Frenet frame of $\alpha$. We say that $\alpha$ is a slant helix if there exists a fixed direction $U$ of $\boldsymbol E_1^3$ such that the function $\langle \boldsymbol N(s),U\rangle$ is constant. In this work we give characterizations of slant helices in terms of the curvature and torsion of $\alpha$. Finally, we discuss the tangent and binormal indicatrices of slant curves, proving that they are helices in $\boldsymbol E_1^3$.

Keywords: Minkowski 3-space, Frenet equations, slant helix

MSC numbers: 53C40, 53C50