Existence of Compatible Contact Structures on $G_2$-manifolds

TL;DR

This paper demonstrates the existence of compatible contact structures on specific $G_2$-manifolds and constructs explicit almost contact metric structures, expanding understanding of geometric structures on these manifolds.

Contribution

It proves the existence of compatible contact structures on certain $G_2$-manifolds and constructs explicit almost contact metric structures, linking contact geometry with $G_2$-structures.

Findings

Existence of contact structures on certain $G_2$-manifolds

Any spin 7-manifold admits an almost contact structure

Explicit constructions of almost contact metric structures

Abstract

In this paper, we show the existence of (co-oriented) contact structures on certain classes of $G_2$-manifolds, and that these two structures are compatible in certain ways. Moreover, we prove that any seven-manifold with a spin structure (and so any manifold with $G_2$-structure) admits an almost contact structure. We also construct explicit almost contact metric structures on manifolds with $G_2$-structures.