Slant helices in Euclidean 4-space $E^4$

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 $\alpha$ 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 pages

References in corpus (2)

• On slant helices in Minkowski space $E_1^3$
• Timelike $B_2$-slant helices in Minkowski space $E_1^4$