On Mannheim partner curves in three dimensional Lie groups
Miskolc Mathematical Notes, vol.15, no.2, pp.467-479, 2014 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 15 Issue: 2
- Publication Date: 2014
- Doi Number: 10.18514/mmn.2014.682
- Journal Name: Miskolc Mathematical Notes
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Page Numbers: pp.467-479
- Keywords: Lie groups, Mannheim curves
- Open Archive Collection: AVESIS Open Access Collection
- Bilecik Şeyh Edebali University Affiliated: Yes
Abstract
In this paper, we define Mannheim partner curves in a three dimensional Lie group G with a bi-invariant metric. The main result of the paper is given as (Theorem 4): A curve α : I ⊂ R→G with the Frenet apparatus {T,N,B,κ,τ} is a Mannheim partner curve if and only if λκ (1+H2)= 1 where λ, μ are constants and H is the harmonic curvature function of the curve α.