A characterization of curves according to parallel transport frame in Euclidean n-space E^n

Abstract

The position vector of a regular curve in Euclidean n-space E n can be written as a linear combination of its parallel transport vectors. In the present study, we characterize such curves in terms of their curvature functions. Further, we obtain some results of constant ratio, T-constant and N-constant type curves in E n .

Associated Curves According to Bishop Frame in 4-Dimensional Euclidean Space

“…Macit and Duldul have defined some new associated curves in 4-dimensional Euclid space andcharacterized every associated curve curvature [8]. Buyukkutuk and Öztürk achieved some results on 4dimensional Euclid space in 2015 [9]. Elzawy studied the Bishop frame and Frenet frame on 4-dimensional Euclid space in his study in 2017 [10].…”

Geometry of Admissible Curves of Constant-Ratio in Pseudo-Galilean Space

“…For the study of constant-ratio curves, the authors gave the necessary and sufficient conditions for curves in Euclidean and Minkowski spaces to become T -constant or N-constant [7][8][9][10]. In analogy with the Euclidean 3-dimensional case, our main goal in this work is to define the spacelike admissible curves of constant-ratio in the pseudo Galilean 3-space as a curve whose position vector always lies in the orthogonal complement N ⊥ of its principal normal vector field N. Consequently, N ⊥ is given by…”

Special Curves According to Bishop Frame in Minkowski 3-Space

“…For example, it may be possible to compute information about the shape of sequences of DNA using a curve defined by the Bishop frame. It also provides a new way to control virtual cameras in computer animation [12]. Some applications of the Bishop frames in Minkowski spaces can be found in [3,4].…”