Weak-(p,k)-Dirac structures

In this paper, we study weak- (p,k) -Dirac structures. Firstly, the definitions of a \wedge ^p-1T^*M -value pairing and a higher Dorfman bracket on the generalized direct sum bundle TM\oplus\wedge ^pT^*M is given. Secondly, the weak -(p,k) -Lagrangian subspace which has more properties than the (p,k) -Lagrangian subspace is constructed. Finally, we define the weak- (p,k) -Dirac structure on smooth manifold M . Many examples of weak- (p,k) -Dirac structure is given. The higher analogue of Courant tensor is discovered.