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On Harmonic Curvatures of Null Curves of the AW(k)-Type in Lorentzian Space

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On Harmonic Curvatures of Null Curves of the AW(k)-Type in Lorentzian Space

Mihriban K¨ulahcı, Mehmet Bektas¸, and Mahmut Erg ¨ut Department of Mathematics, Firat University, 23119 Elazi˘g, Turkey

Reprint requests to M. K.; Fax:+90 424 2330062; E-mail: mihribankulahci@gmail.com Z. Naturforsch.63a,248 – 252 (2008); received December 25, 2007

We investigate null curves of the AW(k)-type (1≤k≤3) in the 3-dimensional Lorentzian space, L3, and give curvature conditions of these curves byusing the Cartan frame. Moreover, we study harmonic curvatures of curves of AW(k)-type and show that if theαFrenet curve is of type AW(1), thenαis a null helix.

Key words:Null Curve; Harmonic Curvature; Frenet Formulas; AW(k)-Type Curve.

MSC 2000:53A04, 53B30, 53C40.

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