Pure Subspaces, Generalizing the Concept of Pure Spinors
arXiv:1310.0104 · doi:10.1016/j.geomphys.2014.03.008
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.
19 pages
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