An Almost Contact Structure on $G_2$-Manifolds

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.