  We compute the zero temperature phase diagram and the Hall response of the
doped perovskite manganites within the model of double exchange and Jahn-Teller
coupling, employing the large dimensionality approximation proposed by Millis
et al. We find that in this scenario a ``hole - like'' $R_H$ for the hole doped
manganites, as observed at low temperature by Matl et al., can be obtained only
when lattice distortions persist in the metallic state at zero temperature. The
calculated temperature dependence of $R_H$ seems to be consistent with the
measured ``normal'' Hall coefficient in thin films.
