This dissertation consists of two main results. First, we investigate the relationship between almost contact structures and G2-structures on seven-dimensional Riemannian manifolds: we show that any manifold with a G2-structure admits an almost contact structure by proving that there exists an almost contact structure on any seven-dimensional manifold with a spin structure. We also construct explicit almost contact structures on manifolds with G2-structures. Moreover, we extend any almost contact structure on an associative submanifold to a G2-manifold. The second part of this thesis shows that contact structures and G2-structures are compatible in certain ways if contact structures exist on a manifold with G2-structures. We also introduce a new structure, which we call a contact-G 2-structure, on a seven-dimensional manifold. Finally, we present examples of a manifold with (torsion free) G2-structures with compatible contact structures.
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