A new example of a compact ERP G2-structure

Abstract

We provide the second known example of an extremally Ricci pinched closed G2-structure on a compact 7-manifold, by finding a lattice in the only unimodular solvable Lie group admitting a left-invariant G2-structure. Furthermore, the Laplacian coflow and its solitons are studied on a 6-parameter family of left-invariant coclosed G2-structures on this Lie group. In this way, we obtain a 4-parameter subfamily of expanding solitons. The family is locally pairwise non-equivalent.

18 pages

References in corpus (3)

• Curvature decomposition of G_2 manifolds
• A class of eternal solutions to the G${}_2$-Laplacian flow
• Explicit Soliton for the Laplacian Co-Flow on a Solvmanifold

Cited by in corpus (2)

• Exact G${}_2$-structures on compact quotients of Lie groups
• Variation formulae for the volume of coassociative submanifolds