A note on closed $G_2$-structures and $3$-manifolds
A note on closed $G_2$-structures and $3$-manifolds
This article shows that given any orientable 3-manifold X, the 7-manifold T^*X \times 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 …