Compatible structures on Lie algebroids and Monge-Ampère operators (Q966466)

This paper is a study of the pairs of structures, for instance Poisson-Nijenhuis structures on a Lie algebroid or Courant algebroid. These structures which are defined by closed 2-forms, Poisson bivectors or (1,1)-tensors with vanishing Nijenhuis torsion, play a central role in the theory of completely integrable systems. They consider the first-order Jacobi differential systems which generalize the Monge-Ampere equations. They then describe the associated geometric structures on 2-dimensional manifolds. They also study the Monge-Ampere operators on 3-dimensional manifolds. Numerous examples are obtained and detailled.