WZW-Poisson manifolds

We observe that a term of the WZW-type can be added to the Lagrangian of the Poisson or sigma-model in such a way that the algebra of the first class constraints remains closed. This leads to a natural generalization of the concept of Poisson geometry. The resulting "WZW-Poisson" manifold M is characterized by a bivector Pi and by a closed three-form H such that 1/2[Pi, Pi](Schouten) = [H, Pi x Pi x Pi]. (C) 2002 Elsevier Science B.V. All rights reserved.