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Harmonic curvatures and generalized helices in En

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

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.

Suggested Citation

  • Camcı, Çetin & İlarslan, Kazım & Kula, Levent & Hacısalihoğlu, H. Hilmi, 2009. "Harmonic curvatures and generalized helices in En," Chaos, Solitons & Fractals, Elsevier, vol. 40(5), pages 2590-2596.
    • Handle: RePEc:eee:chsofr:v:40:y:2009:i:5:p:2590-2596
    DOI: 10.1016/j.chaos.2007.11.001
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    1. El Naschie, M.S., 2005. "Experimental and theoretical arguments for the number and the mass of the Higgs particles," Chaos, Solitons & Fractals, Elsevier, vol. 23(4), pages 1091-1098.
    2. Falcón, Sergio & Plaza, Ángel, 2008. "On the 3-dimensional k-Fibonacci spirals," Chaos, Solitons & Fractals, Elsevier, vol. 38(4), pages 993-1003.
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    1. Külahcı, Mihriban & Bektaş, Mehmet & Ergüt, Mahmut, 2009. "On harmonic curvatures of a Frenet curve in Lorentzian space," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 1668-1675.

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