Harmonic curvatures and generalized helices in E-n

CAMCI Ç., İLARSLAN K., KULA L., Hacisalihoglu H. H.

CHAOS SOLITONS & FRACTALS, vol.40, no.5, pp.2590-2596, 2009 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 40 Issue: 5
  • Publication Date: 2009
  • Doi Number: 10.1016/j.chaos.2007.11.001
  • Journal Name: CHAOS SOLITONS & FRACTALS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.2590-2596
  • Çanakkale Onsekiz Mart University Affiliated: Yes

Abstract

In n-dimensional Euclidean space E-n, harmonic curvatures of a non-degenerate curve defined by Ozdamar and Haci-salihoglu [Ozdamar E, Hacisalihoglu HH. A characterization of Inclined curves in Euclidean n-space. Comm Fac Sci Univ Ankara, Ser A 1 1975;24:15-23]. In this paper, we give some characterizations for a non-degenerate curve alpha to be a generalized helix by using its harmonic curvatures. Also we define the generalized Darboux vector D of a non-degenerate curve alpha in n-dimensional Euclidean space E-n and we show that the generalized Darboux vector D lies in the kernel of Frenet matrix M(s) if and only if the curve a is a generalized helix in the sense of Hayden. (C) 2007 Elsevier Ltd. All rights reserved.