Harmonic curvatures and generalized helices in E-n

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

CHAOS SOLITONS & FRACTALS, cilt.40, sa.5, ss.2590-2596, 2009 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 40 Konu: 5
  • Basım Tarihi: 2009
  • Doi Numarası: 10.1016/j.chaos.2007.11.001
  • Sayfa Sayıları: ss.2590-2596


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.