MMN-682
On Mannheim partner curves in three dimensional Lie groups
Ismail Gök; O. Zeki Okuyucu; Nejat Ekmekci; Yusuf Yayli;Abstract
In this paper, we define Mannheim partner curves in a three dimensional Lie
group $G$ with a bi-invariant metric. And then the main result in this paper
is given as: A curve $\alpha :I\subset \mathbb{R\rightarrow }G$ with the Frenet apparatus $\left \{ T,N,B,\kappa,\tau\right \}$ is a Mannheim partner curve if and only if
\begin{equation*}
\lambda \kappa \left( 1+H^{2}\right) =1
\end{equation*}
where $\lambda $, $\mu $ are constants and $H$ is the harmonic curvature
function of the curve $\alpha .$
Vol. 15 (2014), No. 2, pp. 467-479