Remarks on Poisson reduction on \(k\)-symplectic manifolds (Q1019319)

This paper studies the relation between two reduced standard \(k\)-symplectic Poisson manifolds. Let us recall that the Poisson reduction gives a new Poisson manifold under certain conditions. This well-known procedure has many applications. In this work, the author first presents the usual Poisson reduction of the standard \(k\)-symplectic manifold. Endowing \(T\mathbb R^n\) with a \(k\)-symplectic structure and reducing this structure, the author obtains a new Poisson structure. The relation between the two induced Poisson manifolds is established.