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

Geometry of cotangent bundle of Heisenberg group