ON MANNHEIM PARTNER CURVES IN THREE DIMENSIONAL LIE GROUPS

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

MISKOLC MATHEMATICAL NOTES, cilt.15, sa.2, ss.467-479, 2014 (SCI-Expanded) identifier 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: Mannheim curves, Lie groups, HARMONIC CURVATURES, HELICES, SPACE
  • Ankara 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 ff W I R ! G with the Frenet apparatus fT; N; B; ; g is a Mannheim partner curve if and only if 1CH 2 D 1 where , are constants and H is the harmonic curvature function of the curve ff :