On f-rectifying curves in the Euclidean 4-space

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.