Null (Lightlike) f-Rectifying Curves in the Three Dimensional Minkowski Space ENull (Lightlike) f-Rectifying Curves in the Three Dimensional Minkowski Space $E_1^3$

Abstract

A rectifying curve γ in the Euclidean 3-space $E^3$ is defined as a space curve whose positionvector always lies in its rectifying plane (i.e., the plane spanned by the unit tangent vectorfield Tγ and the unit binormal vector field $B_Y$ of the curve γ), and an f-rectifying curve γ inthe Euclidean 3-space$E^3$is defined as a space curve whose f-position vector γ f, definedby γ f(s) = Rf(s)dγ, always lies in its rectifying plane, where f is a nowhere vanishingreal-valued integrable function in arc-length parameter s of the curve γ. In this paper, weintroduce the notion of f-rectifying curves which are null (lightlike) in the Minkowski3-space $E_1^3$. Our main aim is to characterize and classify such null (lightlike) f-rectifyingcurves having spacelike or timelike rectifying plane in the Minkowski 3-Space $E_1^3$.