Abstract:
In this study, we investigate the explicit characterization of spherical curves using the Flc (Frenet like curve) frame in Euclidean 3-space. Firstly, the axis of curvature and the osculating sphere of a polynomial space curve are calculated using Flc frame invariants. It is then shown that the axis of curvature is on a straight line. The position vector of a spherical curve is expressed with curvatures connected to the Flc frame. Finally, a differential equation is obtained from the third order, which characterizes a spherical curve.