Smarandache curves of Bertrand curves pair according to Frenet frame

Abstract

In this paper, the curvature and the torsion of Smarandache curves obtained by the vectors of the Bertrand partner curve are calculated. These values are expressed depending upon the curve. Besides, we illustrate example with our main results.

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].…”

On Smarandache Curves in Affine 3-Space

“…Another example is Smarandache curves, which are defined as regular curves with the location vector generated by the Frenet vectors of the regular curve. Smarandache curves have been widely studied in different ambient spaces ( [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]).…”

3-Boyutlu Minkowski Uzayında İnvolüt-Evolüt Eğrilerinin T*B* ve N*B* -Smarandache Eğrileri

“…Şenyurt ve Sivas, Öklid uzayında bir eğrinin asli normali ve Darboux vektörünü konum vektörü alarak elde edilen Smarandache eğrilerinin eğriliklerini hesaplamışlardır [9]. Şenyurt vd., Öklid uzayında bazı eğri çiftlerinin Frenet çatısına ve Sabban çatısına göre Smarandache eğrilerini araştırmışlardır [10][11][12][13]. Kalkan vd., 3 1 R involüt-evolüt eğrilerinin Frenet çatısına göre TN -Smarandache eğrilerini incelemişlerdir [7].…”