Generalized Helices in the Euclidean 3-space Through Flow-frame

A representation of time-dependent rotation of a usual Frenet flow is called flow-frame; the angle of rotation is exactly the current parameter. In this paper, we investigate three types of helices in the Euclidean 3-space through flow-frame and give their geometric description with flow-frame apparatus. Then, we introduce the spherical images of a curve by translating flow-frame vectors to the center of the unit sphere in the Euclidean 3-space R-3. Besides, we examine the relationships between a generalized helix and its spherical images.