Abstract
One promising direction for future investigation is the study of almost contact structures on \(G_2\) manifolds. In this paper, we review the properties of special holonomy geometries and almost contact structures. We show that every closed, oriented, smooth 3-manifold has a trivial normal bundle inside a Riemannian 7 manifold with spin structure. We also study the 3-dimensional associative and Harvey–Lawson submanifolds of \(G_2\) manifolds and show that their almost contact structures can be extended to the ambient space.
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