Flat coordinates and dilaton fields for three-dimensional conformal sigma models

General forms of the dilaton fields satisfying the vanishing beta function equations of the sigma models in the flat background can be easily expressed in terms of the Riemannian coordinates. Transformations between group coordinates of three-dimensional conformal sigma models in the flat background and their flat, i.e. Riemannian coordinates are found by solving partial differential equations that follow from the transformation properties of the Levi-Civita connection. By the Poisson-Lie transformation we construct dilatons for the dual sigma models. As the Poisson-Lie transformation does not preserve the geometric properties we get dilatons both in the flat and curved backgrounds. The question if the general flat dilatons fulfil restrictions for construction of dual dilatons is investigated