ON HAMILTONIAN GROUP OF MULTISYMPLECTIC MANIFOLDS

In this paper the Hamiltonian group Ham(M, Ω) is defined for a compact k-plectic manifold (M, Ω) and it is shown that its Lie algebra is the space of equivalence classes of Hamiltonian forms, modulo closed forms. Also if ψ be a multisymplectomorphism in the identity component Msymp0(M, Ω) of the group of multisymplectomorphisms Msymp(M, Ω), we obtain a necessary and sufficient condition under which ψ belongs to Ham(M,Ω). As two consequences, we show that Hamiltonian paths are generated by .(Hamiltonian forms and if Hk(M, R) = 0, then Ham(M, Ω) is equal to Msymp0(M,Ω

Multisymplectic manifold, Hamiltonian group, Hamiltonian vector field