in this paper, we give some characterizations for legendre spherical, legendre normal and legendre rectifying curves in the 3-dimensional sasakian space. furthermore, we show that legendre spherical curves are also legendre normal curves. in particular, we prove that the inverse of curvature of a legendre rectifying curve is a non-constant linear function of the arclength parameter.

In this paper, we characterize the spacelike, the timelike and the null rectifying curves in the Minkowski 3-space in terms of centrodes. In particular, we show that the spacelike and timelike rectifying curves are the extremal curves for which the corresponding function takes its extremal value. On the other hand, we also show that the null rectifying curves are not the extremal curves and giv...

This paper gives new characteristic properties of non-null spherical and rectifying curves in Minkowski 3-space E13. In the light causal characteristics, we give some representations curves. Additionally, proved that tangential function every curve fulfills a third-order differential equation. Then, number well-known rectifying, Lorentzian, hyperbolic are consequences this

The main aim of this paper is to investigate the nature invariance rectifying curve under conformal transformation and obtain a sufficient condition for which such remains conformally invariant. It shown that normal component geodesic curvature homothetic

‎In the present study‎, ‎we consider a regular curve in Galilean‎ ‎$4$-space $mathbb{G}_{4}$ whose position vector is written as a‎ ‎linear combination of its Frenet vectors‎. ‎We characterize such‎ ‎curves in terms of their curvature functions‎. ‎Further‎, ‎we obtain‎ ‎some results of rectifying‎, ‎constant ratio‎, ‎$T$-constant and‎ ‎$N$-constant curves in $mathbb{G}_{4}$‎.

The aim of the paper is to find polynomial parametric equations rectifying Salkowski curves in Minkowski 3-space, via a serial approach. These are characterized by according their curvature; particular those with constant curvature functions and linear harmonic fully characterized. Then, obtained as solutions differential third-order coefficients.