Characterizations of rectifying, normal and osculating curves in three dimensional compact Lie groups
Life Science Journal, vol.10, no.3, pp.819-823, 2013 (Scopus)
- Publication Type: Article / Article
- Volume: 10 Issue: 3
- Publication Date: 2013
- Journal Name: Life Science Journal
- Journal Indexes: Scopus
- Page Numbers: pp.819-823
- Keywords: Lie groups, Normal curves, Osculating curves, Primary 53C40, Rectifying curves, Secondary 22E15
- Bilecik Şeyh Edebali University Affiliated: Yes
Abstract
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.