Geodesic
Spinors in Five-Dimensional Contact Geometry
Symmetry, integrability and geometry: methods and applications, Tome 18 (2022) Cet article a éte moissonné depuis la source Math-Net.Ru

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We use classical (Penrose) two-component spinors to set up the differential geometry of two parabolic contact structures in five dimensions, namely $G_2$ contact geometry and Legendrean contact geometry. The key players in these two geometries are invariantly defined directional derivatives defined only in the contact directions. We explain how to define them and their usage in constructing basic invariants such as the harmonic curvature, the obstruction to being locally flat from the parabolic viewpoint. As an application, we calculate the invariant torsion of the $G_2$ contact structure on the configuration space of a flying saucer (always a five-dimensional contact manifold).
Keywords: spinors, contact geometry, parabolic geometry. 
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     author = {Michael Eastwood and Timothy Moy},
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Michael Eastwood; Timothy Moy. Spinors in Five-Dimensional Contact Geometry. Symmetry, integrability and geometry: methods and applications, Tome 18 (2022). http://geodesic.mathdoc.fr/item/SIGMA_2022_18_a30/

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