Remarks on Hamiltonian structures in G 2-geometry

In this article, we treat G 2-geometry as a special case of multisymplectic geometry and make a number of remarks regarding Hamiltonian multivector fields and Hamiltonian differential forms on manifolds with an integrable G 2-structure; in particular, we discuss existence and make a number of identifications of the spaces of Hamiltonian structures associated to the two multisymplectic structures associated to an integrable G 2-structure. Along the way, we prove some results in multisymplectic geometry that are generalizations of results from symplectic geometry.