Lagrangian calculus on Dirac manifolds

Abstract

We define notions of isotropic, coisotropic and lagrangian submanifolds of Dirac manifolds. Notion of Dirac manifolds, Dirac maps and Dirac relations are defined. Extending the isotropic calculus on presymplectic manifolds and the coisotropic calculus on Poisson manifolds to Dirac manifolds, we construct the lagrangian calculus on Dirac manifolds as an extension of the one on symplectic manifolds. We see that there are three natural categories of Dirac manifolds.