  The position vector field x is the most elementary and natural geometric
object on a Euclidean submanifold $M$. The position vector field plays very
important roles in mathematics as well as in physics. Similarly, the tangential
component x^T of the position vector field is the most natural vector field
tangent to the Euclidean submanifold $M$. We simply call the vector field x^T
the \textit{canonical vector field} of the Euclidean submanifold M.
  In earlier articles, we investigated Euclidean submanifolds whose canonical
vector fields are concurrent, concircular, or torse-forming. In this article we
study Euclidean submanifolds with conformal canonical vector field. In
particular, we characterize such submanifolds. Several applications are also
given. In the last section we present three global results on complete
Euclidean submanifolds with conformal canonical vector field.
