Geometry of cotangent bundle of Heisenberg group (Q6040644)

The paper under review investigates the moduli space \(\mathfrak{M}\) of left-invariant Riemannian metrics on the cotangent bundle of the \((2n+1)\)-dimensional Heisenberg group \(H_{2n+1}\), which classifies inner products on the the associated Lie algebra up to automorphisms. This paper gives an explicit description of \(\mathfrak{M}\), and proves that the complex structure on \(T^*\mathfrak{h}_{2n+1}\) is unique up to automorphisms and sign. Moreover, the corresponding pseudo-Kähler metric is described explicitly and shown to be Ricci-flat.