Harmonic curvatures and generalized helices in En

Çetin Camcı, Kazım İlarslan, Levent Kula and H. Hilmi Hacısalihoğlu

Chaos, Solitons & Fractals, 2009, vol. 40, issue 5, 2590-2596

Abstract: In n-dimensional Euclidean space En, 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 En 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.

Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:40:y:2009:i:5:p:2590-2596

DOI: 10.1016/j.chaos.2007.11.001

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