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 𝐺₂ contact geometry and Legendrean contact geometry. The key players in these two geometries are invariantly defined directional derivatives defined onl...
Збережено в:
| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2022 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2022
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| Онлайн доступ: | 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 |
| Цитувати: | Spinors in Five-Dimensional Contact Geometry. Michael Eastwood and Timothy Moy. SIGMA 18 (2022), 031, 19 pages |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Резюме: | We use classical (Penrose) two-component spinors to set up the differential geometry of two parabolic contact structures in five dimensions, namely 𝐺₂ 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 𝐺₂ contact structure on the configuration space of a flying saucer (always a five-dimensional contact manifold).
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| ISSN: | 1815-0659 |