Moduli of Coassociative Submanifolds and Semi-Flat Coassociative Fibrations
نویسنده
چکیده
We show that the moduli space of deformations of a compact coassociative submanifold L has a natural local embedding as a submanifold of H(L,R). We show that a G2-manifold with a T -action of isomorphisms such that the orbits are coassociative tori is locally equivalent to a minimal 3-manifold in R with positive induced metric where R ∼= H(T ,R). By studying minimal surfaces in quadrics we show how to construct minimal 3-manifold cones in R and hence G2-metrics from equations similar to a set of affine Toda equations. The relation to semi-flat special Lagrangian fibrations and the MongeAmpère equation are explained.
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