In this study, we aim at investigating the geometry of surfaces
corresponding to the geometry of solutions of the geometric curve flows
in Euclidean 3-space R 3 considering the Frenet frame. In particular, we
express some geometric properties and some characterizations of
u-parameter curves and t-parameter curves of some
trajectory surfaces including the Hasimoto surface, shortening
trajectory surface, minimal trajectory surface, τ -normal trajectory
surface in R 3 .