Some characterizations of rectifying curves in the Euclidean space $E^4$

Abstract

In this paper, we define a rectifying curve in the Euclidean 4-space as a curve whose position vector always lies in orthogonal complement $N^{perp}$ of its principal normal vector field N. In particular, we study the rectifying curves in $Bbb{E}^4$ and characterize such curves in terms of their curvature functions.