\(G_{2}\)-structures and octonion bundles (Q507202)

The paper deals with an octonion bundle, which is associated with a \(G_2\)-structure on a 7-dimensional Riemannian manifold. The author discusses the relation of the \(G_2\)-structure with a distinguished octonionic connection. Eventually, the author studies the relation of the octonionic bundle with the spinor bundle and the Dirac operator. Indeed, the author provides a wide motivation for the geometric and physical interest of this framework.