INVARIANT METRICS ON THE IWASAWA MANIFOLD

We compute the automorphism group of the complex three-dimensional Heisenberg Lie algebra and study its action (by isometries) on the set of inner products of ℝ⁶. As a consequence, we give a description of the moduli space of invariant metrics on the Iwasawa manifold. We also show that the action mentioned above is not polar and has a minimal orbit.