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arXiv · 0902.2135

Moduli of Coassociative Submanifolds and Semi-Flat Coassociative Fibrations

David Baraglia
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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-Amp\`ere equation are explained.

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David Baraglia. 2009-02-12. Moduli of Coassociative Submanifolds and Semi-Flat Coassociative Fibrations. https://doi.org/10.1016/j.geomphys.2010.07.006

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