# Slant helices in Euclidean 4-space $E^4$ - Mathematics > Differential Geometry

Slant helices in Euclidean 4-space $E^4$ - Mathematics > Differential Geometry - Download this document for free, or read online. Document in PDF available to download.

Abstract: We consider a unit speed curve $\alpha$ in Euclidean four-dimensional space$E^4$ and denote the Frenet frame by $\{T,N,B 1,B 2\}$. We say that $\alpha$ isa slant helix if its principal normal vector $N$ makes a constant angle with afixed direction $U$. In this work we give different characterizations of suchcurves in terms of their curvatures.

Author: Ahmad T. Ali, Rafael López

Source: https://arxiv.org/