On Mannheim Partner Curves in three Dimensional Lie Groups

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 α with the Frenet apparatus {T,N,B,κ,τ} in G is a Mannheim partner curve if and only if λκ(1+H2)=1, where λ is constant and H is the harmonic curvature function of the curve α.

12 pages. arXiv admin note: text overlap with arXiv:1203.1146