Characterizations of rectifying, normal and osculating curves in three dimensional compact Lie groups

Bozkurt Z., GÖK İ., OKUYUCU O. Z., EKMEKCİ F. N.

Life Science Journal, cilt.10, sa.3, ss.819-823, 2013 (Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 10 Sayı: 3
  • Basım Tarihi: 2013
  • Dergi Adı: Life Science Journal
  • Derginin Tarandığı İndeksler: Scopus
  • Sayfa Sayıları: ss.819-823
  • Anahtar Kelimeler: Lie groups, Normal curves, Osculating curves, Primary 53C40, Rectifying curves, Secondary 22E15
  • Bilecik Şeyh Edebali Üniversitesi Adresli: Evet

Özet

Position vector of a curve provides us some advantages in mechanics, kinematics and differential geometry for characterizations of curves. So, some authors [1, 4, 5, 6] have studied curves whose position vectors always lie their rectifying, normal and osculating plane, respectively. In this paper, we study the rectifying, normal and osculating curves in a three dimensional compact Lie group G with a bi-invariant metric. We give some new characterizations for these curves. Moreover, we obtain necessary and sufficient conditions for them using their harmonic curvature functions.