Direction Curves of Spherical Indicatrices of A New Framed Curve

Authors : İlkay GÜVEN, Fatma ÇOLAK

Pages : 325-339

Doi:10.18185/erzifbed.960608

View : 15 | Download : 13

Publication Date : 2022-03-27

Article Type : Research Paper

Abstract :In this study, direction curves of spherical indicatrix curves (primarily tangent indicatrix) for a curve in three dimensional Euclidean space were investigated. Mentioned curve was given with a new alternative frame which is {N,C,W} frame. It is a new aspect that researching relations between direction curves and the main curve via that new alternative frame. The harmonic curvatures and geodesic curvatures of spherical image of principal normal indicatrix of direction curves were obtained. The general helix, slant helix and C-slant helix characterizations of direction curves were given. Finally these curves with their figures were exemplified.
Keywords : Direction curve, spherical indicatrix curve, alternative frame, helix