Moduli of Coassociative Submanifolds and Semi-Flat Coassociative Fibrations

Abstract

We study the natural structure on the moduli space of deformations of compact coassociative submanifolds. We show that a G2-manifold with a T^4-action of isomorphisms such that the orbits are coassociative tori is locally equivalent to a minimal 3-manifold in R^{3,3} = H^2(T^4,R) with positive induced metric. By studying minimal surfaces in quadrics we show how to construct minimal 3-manifold cones in R^{3,3} and hence G2-metrics from equations similar to a set of affine Toda equations. The relation to semi-flat special Lagrangian fibrations and the Monge-Ampère equation are explained.

25 pages, added section on global aspects

References in corpus (4)

• New aspects of the ddc-lemma
• On the geometry of closed G2-structure
• Duality and Fibrations on G_2 Manifolds
• Coassociative K3 fibrations of compact G_2-manifolds

Cited by in corpus (5)

• Spacelike mean curvature flow
• Toric geometry of $G_2$-manifolds
• Dirichlet problem for maximal graphs of higher codimension
• Cayley fibrations in the Bryant-Salamon $Spin(7)$ manifold
• Variation formulae for the volume of coassociative submanifolds