Closed G2-structures with conformally flat metric

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 ${\mathbb{R}}^7.$

19 pages

References in corpus (1)

• Curvature decomposition of G_2 manifolds