Asian Journal of Mathematics
Volume 17 (2013)
Existence of compatible contact structures on $G_2$-manifolds
Pages: 321 – 334
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.
(almost) contact structures, $G_2$ structures
2010 Mathematics Subject Classification
53C38, 53D10, 53D15, 57R17