Spin(7)-Manifolds and Multisymplectic Geometry

TL;DR

This paper demonstrates that Spin(7)-manifolds with torsion-free structures possess a non-degenerate Cayley four-form, linking Spin(7) geometry to multisymplectic geometry and exploring related Hamiltonian fields.

Contribution

It establishes that Spin(7)-structures can be viewed as multisymplectic, providing new insights into their geometric and Hamiltonian properties.

Findings

Cayley four-form is non-degenerate in multisymplectic sense

Spin(7) geometry is a special case of multisymplectic geometry

Results on Hamiltonian multivector fields and forms

Abstract

We utilize Spin(7) identities to prove that the Cayley four-form associated to 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 to torsion-free Spin(7)-Structures.