Akademik Veri Yönetim Sistemi
Miskolc Mathematical Notes, cilt.17, sa.2, ss.999-1010, 2017 (SCI-Expanded)
© 2017 Miskolc University PressIn this paper, we give the definition of harmonic curvature function some special curves such as helix, slant curves, Mannheim curves and Bertrand curves. Then, we recall thecharacterizations of helices [7], slant curves (see [19]) and Mannheim curves (see [12]) in threedimensional Lie groups using their harmonic curvature function.Moreover, we define Bertrand curves in a three dimensional Lie group G with a bi-invariant metric and the main result in this paper is given as (Theorem 7): A curve (Formula Presented) with the Frenet apparatus {T,N,B,κ,τ} is a Bertrand curve if and only if (Formula Presented) where λ, μ are constants and H is the harmonic curvature function of the curve α.