The intrinsic torsion of SU(3) and G_2 structures

TL;DR

This paper explores the relationship between intrinsic torsion components of SU(3) structures on 6-manifolds and G_2 structures on 7-manifolds, illustrating how certain SU(3) structures can be derived from G_2 holonomy metrics.

Contribution

It provides a detailed analysis of how SU(3) and G_2 structures are interconnected through intrinsic torsion components, with examples demonstrating their geometric relationships.

Findings

Characterization of SU(3) structures as reductions of G_2 holonomy metrics

Examples illustrating possible SU(3) structures from G_2 reductions

Insights into the geometric relationship between 6- and 7-dimensional structures

Abstract

We analyse the relationship between the components of the intrinsic torsion of an SU(3) structure on a 6-manifold and a G_2 structure on a 7-manifold. Various examples illustrate the type of SU(3) structure that can arise as a reduction of a metric with holonomy G_2.