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

Authors : Zafar IQBAL, Joydeep SENGUPTA

Pages : 8-16

Doi:10.33401/fujma.708816

View : 25 | Download : 11

Publication Date : 2020-06-10

Article Type : Research Paper

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 insert ignore into journalissuearticles values(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 $\gamma_finsert ignore into journalissuearticles values(s); = \int finsert ignore into journalissuearticles values(s); d\gamma$, 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 insert ignore into journalissuearticles values(lightlike); in the Minkowski $3$-space $\mathbb{E}^3_1$. Our main aim is to characterize and classify such null insert ignore into journalissuearticles values(lightlike); $f$-rectifying curves having spacelike or timelike rectifying plane in the Minkowski $3$-Space $\mathbb{E}^3_1$.
Keywords : Curvature, Minkowski 3 space, Null lightlike, curve, Rectifying curve, Serret Frenet formulae, Torsion