2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/216834We consider a unit speed curve $α$ in Euclidean four-dimensional space $E^4$ and denote the Frenet frame by $\{T,N,B_1,B_2\}$. We say that $α$ is a slant helix if its principal normal vector $N$ makes a constant angle with a fixed direction $U$. In this work we give different characterizations of such curves in terms of their curvatures.9 pagesDifferential Geometry53C40, 53C50text