On the classification of framed rectifying curves in Euclidean space

Abstract

There are many studies on regular rectifying curves in classical differential geometry, and important results have been obtained. However, these studies are limited for a smooth curve with singular points. To examine such curves and surfaces, the concept of framed curve, which is the general form of regular and Legendre curves, is used. Framed curves are defined as curves that have a moving frame with singular points in Euclidean space. We investigate framed rectifying curves via the dilation of framed curves on S-2 in Double-struck capital R3. Moreover, the result of dilation of framed curves is the framed rectifying curve or not. We give some classifications for the dilation of framed curves. Finally, we give some related examples with their figures.