2 problems

A torsion-free ${\mathrm{Spin}}(7)$-manifold is a Riemannian manifold with torsion-free ${\mathrm{Spin}}(7)$-structure, and a smooth Cayley fibration is a smooth fibration whose fi…

Let $M$ be an $8$-dimensional Riemannian manifold with holonomy $Spin_7$, and let $\Omega^{ch}_M$ denote its chiral de Rham complex. Write $C^\infty(M,\Omega^{ch}_M)$ for the assoc…