A nonlinear transformation between space curves defined by curvature-torsion relations in 3-dimensional Euclidean space

Authors : Emre ÖZTÜRK

Pages : 307-330

Doi:10.31801/cfsuasmas.1083750

View : 38 | Download : 58

Publication Date : 2023-06-23

Article Type : Research Paper

Abstract :In this paper, we define a nonlinear transformation between space curves which preserves the ratio of $\\tau/\\kappa$ of the given curve in 3−dimensional Euclidean space $E^3$. We investigate invariant and associated curves of this transformation by the help of curvature and torsion functions of the base curve. Moreover, we define a new curve insert ignore into journalissuearticles values(family); so-called quasi-slant helix, and we obtain some characterizations in terms of the curvatures of this curve. Finally, we examine some curves in the kinematics, and give the pictures of some special curves and their images with respect to the transformation.
Keywords : Mannheim curve, constant pitch curve, nonlinear transformation, slant helix