Lagrangian calculus on Dirac manifolds (Q2569282)

This paper constructs the Lagrangian calculus on Dirac manifolds as an extension of the symplectic case. The concept of coisotropic submanifold was defined by A. Weinstein. Here, the author defines the notion of isotropic, coisotropic and Lagrangian submanifolds on Dirac structures. Then he extends the isotropic, resp. coisotropic, resp. Lagrangian calculus on symplectic, resp. presymplectic, resp. Poisson manifolds, to that on Dirac manifolds. This leads to three natural categories of Dirac manifolds.