Surfaces in ${\mathbb R}^{N^2-1}$ based on harmonic maps $S^2\to   CP^{N-1}$
  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. 
W.J. Zakrzewski