On the evolution of framed curves in Euclidean 3-space

Abstract

In this paper, we study the evolution of framed curves, which may have singular points. We express flows of framed curves in Euclidean 3-space. We obtain necessary and sufficient conditions as partial differential equations involving the framed curvatures for the inextensible flow of framed curve. Also, we give examples for the evolution equation of framed curvatures.