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

Abstract

In this paper, we investigate the Smarandache curves according to Sabban frame of fixed pole curve which drawn by the unit Darboux vector of the Bertrand partner curve. Some results have been obtained. These results were expressed as the depends Bertrand curve.

On the Sabban frame belonging to involute-evolute curves

“…This curve is called the Smarandache curve [3]. Special Smarandache curves are examined by certain authors [4][5][6][7][8][9]. Taskopru and Tosun [10] studied particular Smarandache curves belonging to Sabban frame on 2 S [10].…”

Some special curves belonging to Mannheim curves pair

“…Senyurt and Caliskan [12] investigated special Smarandache curves in terms of Sabban frame of spherical indicatrix curves and they gave some characterization of Smarandache curves. We investigated special Smarandache curves belonging to Sabban frame drawn on the surface of the sphere by Darboux vector of involute and Bertrand partner curves [13,14]. Let 3 : → I E α be a unit speed curve, we define the quantities of the Frenet frame and Frenet formulae, respectively [15]: S .…”

Smarandache Curves According to Sabban Frame Belonging to Mannheim Curves Pair

“…köprü and Tosun studied special Smarandache curves by means of Sabban frame on S 2 , [8].Şenyurt and Çal¬ skan researched special Smarandache curves according to Sabban frame using spherical indicatrix of a curve and they gave some characterizations of Smarandache curves, [3]. We investigated special Smarandache curves according to Sabban frame drawn on the ON THE SM ARANDACHE CURVE OF M ANNHEIM CURVES 501 surface of a sphere by Darboux vectors of involute and Bertrand partner curves, [7].…”