Slant helices in Minkowski $3$-space $\mathbb{E}_{1}^{3} $ with Sasai's modified frame fields

Abstract

In this paper, we study slant helix using modified orthogonal frame in Minkowski space $\mathbb{E}_{1}^{3}$ with timelike, lightlike and spacelike axes. We also study a general slant helix with the Killing vector field axis. Furthermore, we give a non-trivial example and find the relations for curvature and torsion of $f$-biharmonic slant helix.