Ruled Surfaces According to Bishop Frame in the Euclidean 3-Space

Smarandache Ruled Surfaces According to Bishop Frame in E3

“…Theorem 2.1. see, [3,8] If the unit vector N 1 has a constant angle with the fixed unit vector, then the curve γ is said to be a slant helix. In addition, γ is a slant helix iff…”

“…In addition, some characteristic properties of the ruled surface with Frenet frame of a non-cylindrical ruled surface were investigated in 2020 by Ouarab and Chahdi in [10]. Apart from Frenet frame, in [8] and in [17], Tunc ¸er, (2015) and Masal and Azak, (2019), separately, studied some characteristics of the ruled surfaces according to Bishop frame (introduced by Bishop, 1975 in [2]), whereas Ouarab et al (2018) provided the main properties of ruled surfaces according to alternative frame in [9]. Recently, Ouarab, (2021a) put forth a method to generate new ruled surfaces by taking the advantage of the idea of Smarandache geometry [1,18].…”

On the Resolution of the Acceleration Vector According to Bishop Frame

“…Bishop's framework is used in predicting the structural information of DNA in biology and controlling virtual cameras in the field of Computer Graphics. The readers are referred to the studies [12][13][14][15][16][17][18] which are related to Bishop frame. This article is organized as follows.…”

Simultaneous Developability of Partner Ruled Surfaces according to Darboux Frame in E 3

“…Many geometers have studied some of the differential geometric concepts of the ruled surfaces by means of different moving frames, such as the Frenet-Serret frame, alternative frame, and Bishop frame [6][7][8].…”