Smarandache Curves In Terms of Sabban Frame of Fixed Pole Curve

Abstract

In this paper, we study the special Smarandache curve in terms of Sabban frame of Fixed Pole curve and we give some characterization of Smarandache curves. Besides, we illustrate examples of our results.

Smarandache curves according to Sabban frame of fixed pole curve belonging to the Bertrand curves pair

“…This frame is called the Sabban frame of γ on S 2 (Sphere of unit radius). Then we have the following spherical Frenet formulae of γ, [2,6]…”

“…K. Taşköprü, M. Tosun studied special Smarandache curves according to Sabban frame on S 2 [2]. Ş enyurt and Ç alışkan investigated special Smarandache curves in terms of Sabban frame for fixed pole curve and spherical indicatrix and they gave some characterization of Smarandache curves [4,6]. Let α : I → E 3 be a unit speed curve denote by {T, N, B} the moving Frenet frame.…”

Smarandache Curves of Involute-Evolute Curve According to Frenet Frame

“…In another study, they studied the spatial quaternionic curve and the relationship between Frenet frames of the involute curve of the spatial quaternionic curve which are expressed by using the angle between the Darboux vector and binormal vector [15]. S ¸enyurt et al used special curves as a base to create Smarandache curves, and then studied their geometric properties [12][13][14]. Al-Dayal and Solouma study some properties of spacelike Smarandache curves regarding Bishop frame of a spacelike curve in Minkowski 3-space [1].…”