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Pure subspaces, generalizing the concept of pure spinors

Authors
Journal
Journal of Geometry and Physics
0393-0440
Publisher
Elsevier
Volume
81
Identifiers
DOI: 10.1016/j.geomphys.2014.03.008
Keywords
  • Isotropic Spaces
  • Pure Spinors
  • Integrability
  • Clifford Algebra
  • Twistors
Disciplines
  • Mathematics

Abstract

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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