Closed G2-structures with conformally flat metric

TL;DR

This paper classifies closed G2-structures with conformally flat metrics, showing they are locally equivalent to explicit examples and that complete cases are flat on 7, providing a clear understanding of their geometric structure.

Contribution

It provides a complete classification of closed G2-structures with conformally flat metrics, identifying explicit local models and the uniqueness of the flat structure for complete cases.

Findings

Any closed G2-structure with conformally flat metric is locally one of three explicit types.

Complete conformally flat closed G2-structures are necessarily flat on 7.

The classification simplifies understanding the geometry of such structures.

Abstract

This article classifies closed G2-structures such that the induced metric is conformally flat. It is shown that any closed G2-structure with conformally flat metric is locally equivalent to one of three explicit examples. In particular, it follows from the classification that any closed G2-structure inducing a metric that is both conformally flat and complete must be equivalent to the flat G2-structure on $\mathbb{R}^7.$