On Mannheim Partner Curves in three Dimensional Lie Groups
Differential Geometry
2016-08-14 v1
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 (Theorem 3.3): A curve {\alpha} with the Frenet apparatus {T,N,B,{\kappa},{\tau}} in G is a Mannheim partner curve if and only if {\lambda}{\kappa}(1+H2)=1, where {\lambda} is constant and H is the harmonic curvature function of the curve {\alpha}.
Keywords
Cite
@article{arxiv.1211.6141,
title = {On Mannheim Partner Curves in three Dimensional Lie Groups},
author = {İsmail Gök and O. Zeki Okuyucu and Nejat Ekmekci and Yusuf Yaylı},
journal= {arXiv preprint arXiv:1211.6141},
year = {2016}
}
Comments
12 pages. arXiv admin note: text overlap with arXiv:1203.1146