Geometry of curve flows in isotropic spaces

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. Keywords: Hasimoto surface; Schrodinger flow; extended Harry-Dym flow; isotropic space Mathematics Subject Classification: 53B30, 53C40, 53Z05