Frölicher-Nijenhuis bracket and geometry of $G_2$-and $\mathrm{Spin}(7)$-manifolds

Kotaro Kawai, Hông Vân Lê, Lorenz Schwachhöfer

We extend the characterization of the integrability of an almost complex structure $J$ on differentiable manifolds via the vanishing of the Frölicher-Nijenhuis bracket $[J, J] ^{FN…