A note on closed G_2-structures and 3-manifolds

Authors

HYUNJOO CHO
SEMA SALUR
ALBERT TODD

DOI

10.3906/mat-1310-12

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.

First Page

789

Last Page

795

Recommended Citation

CHO, HYUNJOO; SALUR, SEMA; and TODD, ALBERT (2014) "A note on closed G_2-structures and 3-manifolds," Turkish Journal of Mathematics: Vol. 38: No. 4, Article 15. https://doi.org/10.3906/mat-1310-12
Available at: https://journals.tubitak.gov.tr/math/vol38/iss4/15