Euclidean Curves with Incompressible Canonical Vector Field

Abstract

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