Diffeomorphisms of 7-Manifolds with Coclosed G_2-Structure

TL;DR

This paper introduces new geometric structures related to coclosed G_2-structures on 7-manifolds, establishing their algebraic properties and relationships with morphisms, expanding the understanding of G_2-geometry.

Contribution

It defines coG_2-vector fields, coRochesterian forms, and vector fields, and explores their Lie algebra structures and brackets, providing new tools for G_2-geometry analysis.

Findings

Spaces of coG_2-vector fields and coRochesterian vector fields form Lie subalgebras.

A bracket operation on coRochesterian 2-forms is defined and related to coG_2-morphisms.

The bracket lacks a Jacobi identity but still reveals structural relationships.

Abstract

We introduce coG_2-vector fields, coRochesterian 2-forms and coRochesterian vector fields on manifolds with a coclosed G_2-structure as a continuous of work from [15], and we show that the spaces of coG_2-vector fields and of coRochesterian vector fields are Lie subalgebras of the Lie algebra of vector fields with the standard Lie bracket. We also define a bracket operation on the space of coRochesterian 2-forms associated to the space of coRochesterian vector fields and prove, despite the lack of a Jacobi identity, a relationship between this bracket and so-called coG_2-morphisms.