The geometrization of N-manifolds of degree 2

We discuss how split Poisson N-manifolds of degree 2 are equivalent to self-dual representations up to homotopy and so, following Gracia-Saz and Mehta, to linear splittings of a certain class of VB-algebroids. In other words, the equivalence of categories above induces an equivalence between so called Poisson involutive double vector bundles, which are the dual objects to metric VB-algebroids, and Poisson N-manifolds of degree 2.