Geometry of cotangent bundle of Heisenberg group

In this paper, the classification of left invariant Riemannian metrics on the cotangent bundle of the (2n+1)-dimensional Heisenberg group up to the action of the automorphism group is presented. Moreover, it is proved that the complex structure on this group is unique, and the corresponding pseudo-Kahler metrics are described and shown to be Ricci flat. It is known that this algebra admits an ad-invariant metric of neutral signature. Here, the uniqueness of such metric is proved.(c) 2023 Published by Elsevier B.V.