Spin(7)-manifolds and multisymplectic geometry

Abstract

We utilize Spin(7) identities to prove that the Cayley four-form associated with a torsion-free Spin(7)-structure is non-degenerate in the sense of multisymplectic geometry. Therefore, Spin(7) geometry may be treated as a special case of multisymplectic geometry. We then capitalize on this relationship to make statements about Hamiltonian multivector fields and differential forms associated with torsion-free Spin(7)-structures.