Pure subspaces,generalizing the concept of pure spinors |
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Affiliation: | Departamento de Física, Universidade Federal de Pernambuco, 50670-901 Recife-PE, Brazil |
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Abstract: | The concept of pure spinors 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 the twistor equation to the integrability of maximally isotropic distributions. |
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Keywords: | Isotropic spaces Pure spinors Integrability Clifford algebra Twistors |
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