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, cilt.15, sa.2, ss.467-479, 2014 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 15 Sayı: 2
  • Basım Tarihi: 2014
  • Doi Numarası: 10.18514/mmn.2014.682
  • Dergi Adı: Miskolc Mathematical Notes
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.467-479
  • Anahtar Kelimeler: Lie groups, Mannheim curves
  • Bilecik Şeyh Edebali Üniversitesi Adresli: Evet

Özet

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.