On Mannheim partner curves in three dimensional Lie groups

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GÖK İ., Zeki Okuyucu O. Z., Ekmekci N., YAYLI Y.

Miskolc Mathematical Notes, vol.15, no.2, pp.467-479, 2014 (SCI-Expanded, Scopus) identifier

  • 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.