TY - JOUR
T1 - Moduli of coassociative submanifolds and semi-flat G2-manifolds
AU - Baraglia, D.
PY - 2010/12
Y1 - 2010/12
N2 - 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 G2-manifold with a T4-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 G2-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.
AB - 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 G2-manifold with a T4-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 G2-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.
KW - Coassociative submanifolds
KW - G-manifolds
KW - Torus fibrations
UR - http://www.scopus.com/inward/record.url?scp=77955496675&partnerID=8YFLogxK
U2 - 10.1016/j.geomphys.2010.07.006
DO - 10.1016/j.geomphys.2010.07.006
M3 - Article
SN - 0393-0440
VL - 60
SP - 1903
EP - 1918
JO - Journal of Geometry and Physics
JF - Journal of Geometry and Physics
IS - 12
ER -