Some characterizations of slant helices in the euclidean space En


Ali A. T., Turgut M.

Hacettepe Journal of Mathematics and Statistics, vol.39, no.3, pp.327-336, 2010 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 39 Issue: 3
  • Publication Date: 2010
  • Journal Name: Hacettepe Journal of Mathematics and Statistics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.327-336
  • Keywords: Euclidean n-space, Frenet equations, Slant helices, Type-2 harmonic curvatures
  • Dokuz Eylül University Affiliated: Yes

Abstract

In this work, the notion of a slant helix is extended to the space En. 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.