Characterizations of Framed Curves in Four-Dimensional Euclidean Space

Year 2021, Volume: 4 Issue: 4, 125 - 131, 30.12.2021

Bahar Doğan Yazıcı , Sıddıka Özkaldı Karakuş , Murat Tosun

https://doi.org/10.32323/ujma.1008148

Cited By: 8

Abstract

Framed curves in Euclidean space are used to investigate singular curves and are important
for singularity theory. In this study, framed curves in four-dimensional Euclidean space are
introduced and new results are obtained. The relation of framed curves with Frenet curves
in four-dimensional Euclidean space is given and Bishop-type frame of framed curves is
introduced with the help of Euler angles. In addition, by using Bishop-type framed curves in
four-dimensional Euclidean space, framed rectifying curves, framed osculating curves and
framed normal curves are introduced. Also, some characterizations depending on framed
curvatures are obtained.

Keywords

Euler angles , Bishop-type framed curves , Framed curves in R4

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