  In 1992, P. Pol\'{a}\v{c}ik\cite{P2} showed that one could linearly imbed any
vector fields into a scalar semi-linear parabolic equation on $\Omega$ with
Neumann boundary condition provided that there exists a smooth vector field
$\Phi=(\phi_{1},...,\phi_{n}) $ on $\bar{\Omega}$ such that \[
\left\{\begin{array} [c]{l}% \operatorname*{rank}(\Phi(x) ,\partial_{1}\Phi(x)
,...,\partial_{n}\Phi(x)) =n\text{for all}x\in\bar{\Omega},
\frac{\partial\Phi}{\partial\nu}=0\text{on}\partial\Omega\text{.}% \end{array}
\right. \] In this short note, we give a classification of all the domains on
which one may find such type of vector fields.
