Null (Lightlike) $f$-Rectifying Curves in the Three Dimensional Minkowski Space $\mathbb{E}^3_1$

Abstract

A rectifying curve $\gamma$ in the Euclidean $3$-space $\mathbb{E}^3$ is defined as a space curve whose position vector always lies in its rectifying plane (i.e., the plane spanned by the unit tangent vector field $T_\gamma$ and the unit binormal vector field $B_\gamma$ of the curve $\gamma$), and an $f$-rectifying curve $\gamma$ in the Euclidean $3$-space $\mathbb{E}^3$ is defined as a space curve whose $f$-position vector $\gamma_f$, defined by $\gamma_f(s) = \int f(s) d\gamma$, always lies in its rectifying plane, where $f$ is a nowhere vanishing real-valued integrable function in arc-length parameter $s$ of the curve $\gamma$. In this paper, we introduce the notion of $f$-rectifying curves which are null (lightlike) in the Minkowski $3$-space $\mathbb{E}^3_1$. Our main aim is to characterize and classify such null (lightlike) $f$-rectifying curves having spacelike or timelike rectifying plane in the Minkowski $3$-Space $\mathbb{E}^3_1$.