Multisymplectic 3-forms on 7-dimensional manifolds

TL;DR

This paper characterizes 7-dimensional manifolds admitting various types of multisymplectic 3-forms, extending previous work on G2-structures to other algebraic types, thereby broadening understanding of their geometric structures.

Contribution

It provides a comprehensive characterization of manifolds with different multisymplectic 3-forms beyond the G2 case, filling gaps in the existing classification.

Findings

Characterization of manifolds with specific multisymplectic 3-forms

Extension of classification to remaining algebraic types

Advancement in understanding geometric structures on 7-manifolds

Abstract

The goal of the paper is to give characterization of closed connected manifolds which admit a global multisympletic 3-form of some algebraic type. A generic type of such 3-form is equivalent to a G2-structure. This is the most interesting case and was solved in [Gr]. Some other algebraic types were solved quite recently. In this paper we give characterization in the remaining cases.