Spinors in Five-Dimensional Contact Geometry

We use classical (Penrose) two-component spinors to set up the differential geometry of two parabolic contact structures in five dimensions, namely ₂ contact geometry and Legendrean contact geometry. The key players in these two geometries are invariantly defined directional derivatives defined only...

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Veröffentlicht in:Symmetry, Integrability and Geometry: Methods and Applications
Datum:2022
ISSN:1815-0659
Hauptverfasser: Eastwood, Michael, Moy, Timothy
Format: Artikel
Sprache:Englisch
Veröffentlicht: Інститут математики НАН України 2022
Online Zugang:https://nasplib.isofts.kiev.ua/handle/123456789/211637
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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Zitieren:Spinors in Five-Dimensional Contact Geometry. Michael Eastwood and Timothy Moy. SIGMA 18 (2022), 031, 19 pages

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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Zusammenfassung:We use classical (Penrose) two-component spinors to set up the differential geometry of two parabolic contact structures in five dimensions, namely 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 ₂ contact structure on the configuration space of a flying saucer (always a five-dimensional contact manifold).
ISSN:1815-0659