On Mannheim Partner Curves in three Dimensional Lie Groups
\.Ismail G\"ok, O. Zeki Okuyucu, Nejat Ekmekci, Yusuf Yayl{\i}
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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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