Spin(7)-manifold

Summary

A Spin(7)-manifold is a Riemannian manifold of dimension $8$ whose holonomy group lies in the group $\operatorname{Spin}(7)$, viewed inside $SO(8)$. The structure is encoded in a parallel $4$-form, the Cayley form. Spin(7)-manifolds are Ricci-flat and form, with $G_2$ manifolds, the two exceptional cases of Berger's list.