G2-structure deformations and warped products

Abstract

We overview the properties of non-infinitesimal deformations of G2-structures on seven-manifolds, and in particular, focus on deformations that lie in the seven-dimensional representation of G2 and are thus defined by a vector. We then consider deformations from G2-structures with the torsion class having one-dimensional and seven-dimensional components (so-called conformally nearly parallel G2-manifolds) to G2-structures with just a one-dimensional torsion component (nearly parallel G2-manifolds). We find that deformations between such structures exist if and only if the metric is a particular warped product metric.

13 pages, v2 - corrected typos, clarified proof of Thm 4.4, updated references

References in corpus (3)

• Flows of G_2 Structures, I
• Moduli spaces of G2 manifolds
• Conformal equivalence between certain geometries in dimension 6 and 7

Cited by in corpus (1)

• Short-time behaviour of a modified Laplacian coflow of G2-structures