- Turkish Journal of Mathematics and Computer Science
- Vol: 13 Issue: 2
- (k,m)-type Slant Helices According to Parallel Transport Frame in Euclidean 4-Space
(k,m)-type Slant Helices According to Parallel Transport Frame in Euclidean 4-Space
Authors : Fatma BULUT, Feyzi TARTIK
Pages : 261-269
Doi:10.47000/tjmcs.858489
View : 6 | Download : 2
Publication Date : 2021-12-31
Article Type : Research
Abstract :In this work, we describe a Frenet frame in 4-dimensional Euclidean space and call this frame as parallel transport frame (PTF). PTF is an alternative approach to defining a moving frame. This frame is obtained by rotating the tangent vector and the first binormal vector of a unit speed curve by an euler angle and then we give curvature functions according to PTF of the curve. Also, we introduce $(k,m)$-type slant helices according to PTF in Euclidean 4-Space. Additionally, we obtain the characterization of slant helices according to this frame in $\mathbb{E}^{4}$ and give an example of our main result.Keywords : Slant helix, curvatures, Euclidean 4-space, parallel transport frame