Existence of Compatible Contact Structures on $G_2$-manifolds

Details Existence of Compatible Contact Structures on $G_2$-manifolds Existence of Compatible Contact Structures on $G_2$-manifolds

2011-12-13

arxiv.org/abs/1112.2951v1

Mathematics

Differential Geometry

15 pages

Scientific paper

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.

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