  We study quasiisometries between negatively curved homogeneous manifolds
associated with diagonalizable derivations on Heisenberg algebras. We classify
these manifolds up to quasiisometry, and show that all quasiisometries between
such manifolds (except when they are complex hyperbolic spaces) are almost
similarities. We prove these results by studying the quasisymmetric maps on the
ideal boundary of these manifolds.
