The Symplectic Geometry Problem with n-plectic Structure

The symplectic geometry problem with n-plectic structure is proposed based on previous studies. The vector fields(n-plectic vector field, n-Hamiltonian vector field)on n-plectic manifolds are discussed, and the two necessary and sufficient conditions for n-plectic vector field are given according to the property of Lie derivative, meanwhile, the result that two n-Hamiltonian vector field in integrated bracket is still an n-Hamiltonian vector field is given. Finally, the short exact sequences are obtained by defining linear maps.