A GEOMETRY FOR MULTIDIMENSIONAL INTEGRABLE SYSTEMS

A deformed differential calculus is developed based on an associative star-product. In two dimensions the Hamiltonian vector fields model th e algebra of pseudo-differential operator, as used in the theory of in tegrable systems. Thus one obtains a geometric description of the oper ators. A dual theory is also possible, based on a deformation of diffe rential forms. This calculus is applied to a number of multidimensiona l integrable systems such as the KP hierarchy, thus obtaining a geomet rical description of these systems. The limit in which the deformation disappears corresponds to taking the dispersionless limit in these hi erarchies.