Turkish Journal of Mathematics
Abstract
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 submanifold of T^*X \times R such that \varphi _{N^*S}\equiv 0. A corollary of the proof of this result is that N^*S \times R is a 4-dimensional submanifold of T^*X \times R such that \varphi _{N^*S \times R}\equiv 0.
DOI
10.3906/mat-1310-12
First Page
789
Last Page
795
Recommended Citation
CHO, H, SALUR, S, & TODD, A (2014). A note on closed G_2-structures and 3-manifolds. Turkish Journal of Mathematics 38 (4): 789-795. https://doi.org/10.3906/mat-1310-12
