Moduli of coassociative submanifolds and semi-flat G2-manifolds
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2010
Authors
Baraglia, D.
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Journal of Geometry and Physics, 2010; 60(12):1903-1918
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D. Baraglia
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We show that the moduli space of deformations of a compact coassociative submanifold C has a natural local embedding as a submanifold of H2(C,R). We show that a G<inf>2</inf>-manifold with a T<sup>4</sup>-action of isometries such that the orbits are coassociative tori is locally equivalent to a minimal 3-manifold in R3,3 with positive induced metric where R3,3~=H2(T4,R). By studying minimal surfaces in quadrics we show how to construct minimal 3-manifold cones in R3,3 and hence G<inf>2</inf>-metrics from a real form of the affine Toda equations. The relations to semi-flat special Lagrangian fibrations and the Monge-Ampère equation are explained. © 2010 Elsevier B.V.
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© 2010 Elsevier B.V. All rights reserved.