Harmonic curvatures and generalized helices in E-n

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.