Bertrand Curves in three Dimensional Lie Groups

Abstract

In this paper, we give the defination of harmonic curvature function some special curves such as helix, slant curves, Mannheim curves and Bertrand curves. Then, we recall the characterizations of helices [8], slant curves (see [19]) and Mannheim curves (see [12]) in three dimensional Lie groups using their harmonic curvature function. Moreover, we define Bertrand curves in a three dimensional Lie group G with a bi-invariant metric and the main result in this paper is given as (Theorem 3.4): A curve ?α with the Frenet apparatus {T,N,B,κ,τ} in G is a Bertrand curve if and only if λκ+μκH=1 where λ,μ ? are constants and H is the harmonic curvature function of the curve α.

11 pages. arXiv admin note: substantial text overlap with arXiv:1211.6141, arXiv:1203.1146

References in corpus (1)

• Slant helices in three dimensional lie groups

Cited by in corpus (1)

• Ruled Surfaces in Three Dimensional Lie Groups