  We investigate the geometric characteristics of constant gaussian curvature
surfaces obtained from solutions of the $G(m,n)$ sigma model. Most of these
solutions are related to the Veronese sequence. We show that we can distinguish
surfaces with the same gaussian curvature using additional quantities like the
topological charge and the mean curvature. The cases of
$G(1,n)=\mathbb{C}P^{n-1}$ and $G(2,n)$ are used to illustrate these
characteristics.
