(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 : 10 | Download : 6

Publication Date : 2021-12-31

Article Type : Research Paper

Abstract :In this work, we describe a Frenet frame in 4-dimensional Euclidean space and call this frame as parallel transport frame insert ignore into journalissuearticles values(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 $insert ignore into journalissuearticles values(k,m);$-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