Remarks on Hamiltonian Structures in G_2-Geometry

TL;DR

This paper explores Hamiltonian structures within G_2-geometry by framing it as multisymplectic geometry, discussing existence, identifications, and generalizing symplectic results to the multisymplectic context.

Contribution

It introduces a multisymplectic perspective on G_2-geometry, analyzing Hamiltonian multivector fields and forms, and extends symplectic results to this broader setting.

Findings

Identified spaces of Hamiltonian structures in G_2-geometry

Proved generalizations of symplectic geometry results in multisymplectic context

Discussed existence conditions for Hamiltonian multivector fields

Abstract

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.