In the present study we consider Euclidean curves with incompressible canonicalvector fields. We investigate such curves in terms of their curvature functions. Recently,B.Y. Chen gave classification of plane curves with incompressible canonical vectorfields. For higher dimensional case we gave a complete classification of Euclideanspace curves with incompressible canonical vector fields. Further we obtain someresults of the Euclidean curves with incompressible canonical vector fields in 4 -dimensional Euclidean space E4
