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 rectifying space (i.e., the orthogonal complement N_γ ˔ of its principal normal vector field N_γ) 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 γ_f, defined by γ_f (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.