Mannheim Partner Curves in Cartan-Vranceanu 3-space

Abstract

In this paper, the Mannheim mate curves of the proper biharmonic
curves in Cartan-Vranceanu 3-dimensional spaces $(M,ds_{l,m}^{2})$, with
$l^{2}\neq 4m $ and $m\neq 0$ are studied. We give the definition of the Mannheim mate of a proper biharmonic curve and give the explicit parametric equations of that Mannheim mate curve in Cartan-Vranceanu 3-dimensional space. Moreover, we show that the distance between corresponding points of the Mannheim pairs is constant in Cartan-Vranceanu
3-dimensional spaces.