Cohomogeneity-one $G_2$-Laplacian flow on 7-torus

Abstract

We prove the hypersymplectic flow of simple type on standard torus ${\mathbb{T}}^4$ exists for all time and converges to the standard flat structure modulo diffeomorphisms. This result in particular gives the first example of a cohomogeneity-one $G_2$-Laplacian flow on a compact $7$-manifold which exists for all time and converges to a torsion-free $G_2$ structure modulo diffeomorphisms.

v2, typos corrected, version appeared in the Journal of the London Mathematical Society

References in corpus (2)

• Hypersymplectic 4-manifolds, the $G_2$-Laplacian flow and extension assuming bounded scalar curvature
• Boundary value problems in dimensions seven, four and three related to exceptional holonomy

Cited by in corpus (6)

• On the automorphism group of a closed G${}_2$-structure
• A class of eternal solutions to the G${}_2$-Laplacian flow
• Curvature pinching estimate under the Laplacian G_{2} flow
• On $G_2$-structures, special metrics and related flows
• Hypersymplectic Structures Invariant Under an Effective Circle Action
• Real analyticity of the modified Laplacian coflow