MMN-1314
Bertrand curves in three dimensional Lie groups
O. Zeki Okuyucu; Ismail Gök; Yusuf Yayli; Nejat Ekmekci;Abstract
In 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 the characterizations of helices [8], slant curves (see [19]) and Mannheim curves (see [12]) in three dimensional 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 3.4): A curve α :I⊆ℝ→G with Frenet apparatus {T,N,B,κ,τ}is a Bertrand curve if and only if
λκ+μκH=1
where λ,μ are constants and H is the harmonic curvature function of the curve α.
Vol. 17 (2016), No. 2, pp. 999-1010
DOI: 10.18514/MMN.2017.1314