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

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.