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

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

2009-01-21

arxiv.org/abs/0901.3324v1

Mathematics

Differential Geometry

9 pages

Scientific paper

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.

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