  In this paper the classification of left-invariant Riemannian metrics, up to
the action of the automorphism group, on cotangent bundle of (2n+1)-dimensional
Heisenberg group is presented. Also, it is proved that the complex structure on
that group is unique and the corresponding pseudoK\"ahler metrics are described
and shown to be Ricci flat. It is well known that this algebra admits an
ad-invariant metric of neutral signature. Here, the uniqueness of such metric
is proved
