Pure Subspaces, Generalizing the Concept of Pure Spinors

Abstract: The concept of pure spinor is generalized, giving rise to the notion of pure subspaces, spinorial subspaces associated to isotropic vector subspaces of non-maximal dimension. Several algebraic identities concerning the pure subspaces are proved here, as well as some differential results. Furthermore, the freedom in the choice of a spinorial connection is exploited in order to relate twistor equation to the integrability of maximally isotropic distributions.