On some involution theorems on twofold Poisson manifolds
The author points out some involution theorems which are consequences of the existence of two compatible Poisson structures on a smooth manifold. Also using a theorem of Lichnerowicz on local triviality of the Schouten- Nijenhuis cohomology, he shows that the local exactness of a second Poisson structure with respect to the first one is equivalent with the involutivity of the algebra of smooth invariant functions of the first Poisson structure.
scientific article; zbMATH DE number 4064108