An Almost Contact Structure on $G_2$-Manifolds

TL;DR

This paper investigates an almost contact metric structure on $G_2$-manifolds, characterizes when it is cosymplectic, and constructs an almost contact metric 3-structure on closed $G_2$-manifolds, analyzing its properties.

Contribution

It characterizes the cosymplectic condition for the almost contact structure on $G_2$-manifolds and explicitly constructs an almost contact metric 3-structure on closed $G_2$-manifolds.

Findings

Characterization of cosymplectic almost contact structures on $G_2$-manifolds

Explicit construction of almost contact metric 3-structure on closed $G_2$-manifolds

Conditions for the 3-structure to be 3-cosymplectic

Abstract

In this article, we study an almost contact metric structure on a $G_2$-manifold constructed by Arikan, Cho and Salur in via the classification of almost contact metric structures given by Chinea and Gonzalez. In particular, we characterize when this almost contact metric structure is cosymplectic and narrow down the possible classes in which this almost contact metric structure could lie. Finally, we show that any closed $G_2$-manifold admits an almost contact metric $3$-structure by constructing it explicitly and characterize when this almost contact metric $3$-structure is $3$-cosymplectic.