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arXiv · 1211.6141

On Mannheim Partner Curves in three Dimensional Lie Groups

İsmail Gök·O. Zeki Okuyucu·Nejat Ekmekci·Yusuf Yaylı
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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}.

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İsmail Gök, O. Zeki Okuyucu, Nejat Ekmekci, Yusuf Yaylı. 2012-11-26. On Mannheim Partner Curves in three Dimensional Lie Groups. https://arxiv.org/abs/1211.6141

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