Almost contact structures on manifolds with a $G_2$ structure

Xenia de la Ossa; Magdalena Larfors; Matthew Magill

paper

Almost contact structures on manifolds with a $G_{2}$ structure

arXiv:2101.12605

Abstract

We review the construction of almost contact metric (three-) structures, abbreviated ACM(3)S, on manifolds with a $G_{2}$ structure. These are of interest for certain supersymmetric configurations in string and M-theory. We compute the torsion of the $S U (3)$ structure associated to an ACMS and apply these computations to heterotic $G_{2}$ systems and supersymmetry enhancement. We initiate the study of the space of ACM3Ss, which is an infinite dimensional space with a local product structure and interesting topological features. Tantalising links between ACM3Ss and associative and coassociative submanifolds are observed.

61 pages. v3: References added, minor revision v2: References added

Almost contact structures on manifolds with a G2​ structure

Abstract

Almost contact structures on manifolds with a $G_{2}$ structure