<abstract xmlns="http://www.w3.org/1999/xhtml">

A rectifying curve in the Euclidean 4-space 𝔼4 is defined as an arc length parametrized curve γ in 𝔼4 such that its position vector always lies in its rectifying space (i.e., the orthogonal complement Nγ ˔ of its principal normal vector field Nγ) in 𝔼4. In this paper, we introduce the notion of an f-rectifying curve in 𝔼4 as a curve γ in 𝔼4 parametrized by its arc length s such that its f-position vector γf, defined by γf (s) = ∫ f(s)dγ for all s, always lies in its rectifying space in 𝔼4, where f is a nowhere vanishing integrable function in parameter s of the curve γ. Also, we characterize and classify such curves in 𝔼4.
</abstract>

A rectifying curve in the Euclidean 4-space 𝔼4 is defined as an arc length parametrized curve γ in 𝔼4 such that its position vector always lies in its rectifying space (i.e., the orthogonal complement Nγ ˔ of its principal normal vector field Nγ) in 𝔼4. In this paper, we introduce the notion of an f-rectifying curve in 𝔼4 as a curve γ in 𝔼4 parametrized by its arc length s such that its f-position vector γf, defined by γf (s) = ∫ f(s)dγ for all s, always lies in its rectifying space in 𝔼4, where f is a nowhere vanishing integrable function in parameter s of the curve γ. Also, we characterize and classify such curves in 𝔼4.

On f-rectifying curves in the Euclidean 4-space

Acta Universitatis Sapientiae, Mathematica

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

{"article-title":"On f-rectifying curves in the Euclidean 4-space"}

A rectifying curve in the Euclidean 4-space 𝔼4 is defined as an arc length parametrized curve γ in 𝔼4 such that its position vector always lies in its...

On f-rectifying curves in the Euclidean 4-space

Published Online: Aug 26, 2021

Page range: 192 - 208

Received: Jun 27, 2020

DOI: https://doi.org/10.2478/ausm-2021-0011

Keywords
Euclidean 4-space, Frenet formulae, rectifying curve, curvature

© 2021 Zafar Iqbal et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

On f-rectifying curves in the Euclidean 4-space

Published Online: Aug 26, 2021

Page range: 192 - 208

Received: Jun 27, 2020

DOI: https://doi.org/10.2478/ausm-2021-0011

KeywordsEuclidean 4-space, Frenet formulae, rectifying curve, curvature

© 2021 Zafar Iqbal et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
Euclidean 4-space, Frenet formulae, rectifying curve, curvature