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 2 l,m), with l 2 4m and m 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.

Mannheim partner curves in the special linear group

“…Okuyucu and Yazici (2022), give a new approach for Bertrand and Mannheim curves in 3D Lie groups with bi-invariant metrics. Among others recent studies are Orbay and Kasap (2009), Tul and Sariog ľugil (2011), Ceylan and Ergin (2016), Senyurt et al (2017a, b), Senyurt (2012) and Has and Yilmaz (2021).…”

“…Let ( ) be a Mannheim pair in SL(2, ). The distance between corresponding points of and is constant, that is, is nonzero constant (Ceylan and Ergin, 2016).…”