Geometry of curve flows in isotropic spaces

Abstract

In this paper, we study inextensible flows of a curve in an isotropic 3-space and give a necessary and sufficient condition for inextensible flows of the curve as a partial differential equation involving the curvatures of the curve. Using binormal flows of a space curve we give the Backlund transformations of the Schrodinger flows and the extended Harry-Dym flows. Finally, we investigate some geometric properties of Hasimoto surfaces which wiped out by the Schrodinger flows.