  It is shown that the Pohlmeyer map of a $\sigma$-model with a toric
two-dimensional target space naturally leads to the `sausage' metric. We then
elaborate the trigonometric deformation of the $\mathrm{CP}^{n-1}$-model,
proving that its $T$-dual metric is K\"ahler and solves the Ricci flow
equation. Finally, we discuss a relation between flag manifold $\sigma$-models
and Toda field theories.
