  We show that many surfaces in $\R^{N^2-1}$ can be generated by harmonic maps
of $S^2\to CP^{N-1}$. These surfaces are based on the projectors in $CP^{N-1}$
which describe maps of $S^2\to CP^{N-1}$. In the case when these maps form the
Veronese sequence all the surfaces have constant curvature.
