Spin(7)-Manifolds and Multisymplectic Geometry
Differential Geometry
2022-01-12 v1 Mathematical Physics
math.MP
Symplectic Geometry
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.
Cite
@article{arxiv.2110.05685,
title = {Spin(7)-Manifolds and Multisymplectic Geometry},
author = {Aaron Kennon},
journal= {arXiv preprint arXiv:2110.05685},
year = {2022}
}
Comments
17 pages, no figures