(k,m)-type Slant Helices According to Parallel Transport Frame in Euclidean 4-Space

Year 2021, Volume: 13 Issue: 2, 261 - 269, 31.12.2021

Fatma Bulut Feyzi Tartık

https://doi.org/10.47000/tjmcs.858489

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

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