An Explicit Construction of Self-dual 2-forms in Eight Dimensions

Abstract

The geometry of self-dual 2-forms in eight dimensions is studied. These 2-forms determine an $n^2-n+1$ dimensional manifold ${\mathcal{S}}_{2n}$. We prove that for add $n$, it has only one dimensionallinear subspaces. In eight dimensions, the self-dual forms of Corrigan et al constitue a seven dimensional linear subspace of ${\mathcal{S}}_8$, among many other intersting linear subspaces.