We show that for some negatively curved solvable Lie groups, all self
quasiisometries are almost isometries. We prove this by showing that all self
quasisymmetric maps of the ideal boundary (of the solvable Lie groups) are
bilipschitz with respect to the visual metric. We also define parabolic visual
metrics on the ideal boundary of Gromov hyperbolic spaces and relate them to
visual metrics.