Some characterizations of slant helices in the Euclidean space $E^n$

Abstract

In this work, the notion of a slant helix is extended to the space $Bbb {E}^ n$. First, we introduce the type-2 harmonic curvatures of a regular curve. Thereafter, by using this, we present some necessary and sufficient conditions for a curve to be a slant helix in Euclidean n-space. We also express some integral characterizations of such curves in terms of the curvature functions. Finally, we give some characterizations of slant helices in terms of type-2 harmonic curvatures.