Harmonic curvatures and generalized helices in EnEn

In n  -dimensional Euclidean space EnEn, harmonic curvatures of a non-degenerate curve defined by Özdamar and Hacisalihoğlu [Özdamar E, Hacısalihoglu HH. A characterization of Inclined curves in Euclidean n-space. Comm Fac Sci Univ Ankara, Ser A1 1975;24:15–23]. In this paper, we give some characterizations for a non-degenerate curve α to be a generalized helix by using its harmonic curvatures. Also we define the generalized Darboux vector D of a non-degenerate curve α in n  -dimensional Euclidean space EnEn and we show that the generalized Darboux vector D lies in the kernel of Frenet matrix M(s) if and only if the curve α is a generalized helix in the sense of Hayden.