A Note on Closed G_2-Structures and 3-Manifolds

Details A Note on Closed G_2-Structures and 3-Manifolds A Note on Closed G_2-Structures and 3-Manifolds

2011-12-05

arxiv.org/abs/1112.0830v1

Mathematics

Differential Geometry

7 pages, LaTex

Scientific paper

This article shows that given any orientable 3-manifold X, the 7-manifold T^*X x R admits a closed G_2-structure varphi=Re(Omega)+omega\wedge dt where Omega is a certain complex-valued 3-form on T^*X; next, given any 2-dimensional submanifold S of X, the conormal bundle N^*S of S is a 3-dimensional submanifold of T^*X x R such that varphi restricted to N^*S is equivalent to 0. A corollary of the proof of this result is that N^*S x R is a 4-dimensional submanifold of T^*X x R such that varphi restricted to N^*S x R is equivalent to 0.

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