2-PLECTIC MANIFOLDS AND ITS RELATION WITH COURANT ALGEBROIDS

In this paper we study the relation between 2-plectic manifolds and Courant algebroids. We establish a relation between 2-Lagrangian submanifolds of 2-plectic manifolds and subbundles of Courant algebroids. Also we show that an action of a compact Lie group G on a 2-plectic manifold (M, omega) can be extended to an action of G on an exact Courant algebroid E over M if and only if G is a subgroup of Hamiltonian group of (M, omega).