The classification of ERP G2-structures on Lie groups

TL;DR

This paper classifies all left-invariant closed G2-structures on Lie groups that are extremally Ricci pinched, identifying five distinct cases with specific properties, including exactness and unimodularity.

Contribution

It provides a complete classification of extremally Ricci pinched closed G2-structures on Lie groups, highlighting five unique examples and their geometric properties.

Findings

Five distinct extremally Ricci pinched G2-structures identified

All but one G2-structure are exact

The unimodular case is the only non-exact example

Abstract

A complete classification of left-invariant closed G2-structures on Lie groups which are extremally Ricci pinched, up to equivalence and scaling, is obtained. There are five of them, they are defined on five different completely solvable Lie groups and the G2-structure is exact in all cases except one, given by the only example in which the Lie group is unimodular.