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 [2] via the classification of almost contact metric structures given by Chinea and Gonzalez [14]. 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.

Almost Contact Metric Structures Induced by $G_2$ Structures

“…If ∇ϕ = 0, then it can be seen that ∇Φ = 0 if and only if ∇ξ = 0 [2,14]. If ξ is a Killing vector field on a manifold with any G 2 structure, then…”

“…proved the existence of almost contact metric structures on manifolds with G 2 structures [4]. Todd studied almost contact metric structures on manifolds with parallel G 2 structures [14].…”