  Transformations between group coordinates of three--dimensional conformal
sigma models in the flat background and their flat, i.e. Riemannian coordinates
enable to find general dilaton fields for three-dimensional flat sigma models.
By the Poisson-Lie transformation we can get dilatons for the dual sigma models
in a curved background. Unfortunately, in some cases the dilatons depend on
inadmissible auxiliary variables so the procedure is not universal. The cases
where the procedure gives proper and nontrivial dilatons in curved backgrounds
are investigated and results given.
