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...
Збережено в:
| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Дата: | 2022 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2022
|
| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/211637 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| 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| _version_ | 1862601836427476992 |
|---|---|
| author | Eastwood, Michael Moy, Timothy |
| author_facet | Eastwood, Michael Moy, Timothy |
| citation_txt | Spinors in Five-Dimensional Contact Geometry. Michael Eastwood and Timothy Moy. SIGMA 18 (2022), 031, 19 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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).
|
| first_indexed | 2026-03-14T02:56:19Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211637 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-14T02:56:19Z |
| publishDate | 2022 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Eastwood, Michael Moy, Timothy 2026-01-07T13:42:47Z 2022 Spinors in Five-Dimensional Contact Geometry. Michael Eastwood and Timothy Moy. SIGMA 18 (2022), 031, 19 pages 1815-0659 2020 Mathematics Subject Classification: 53B05; 53D10; 58J10 arXiv:2201.13048 https://nasplib.isofts.kiev.ua/handle/123456789/211637 https://doi.org/10.3842/SIGMA.2022.031 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). We would like to thank all staff at SIGMA in Kyiv for their extraordinary courage, continuing their work despite the shocking Russian invasion and unconscionable aggression. We would also like to thank the referees for their careful reading of our manuscript and for their valuable suggestions and corrections. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Spinors in Five-Dimensional Contact Geometry Article published earlier |
| spellingShingle | Spinors in Five-Dimensional Contact Geometry Eastwood, Michael Moy, Timothy |
| title | Spinors in Five-Dimensional Contact Geometry |
| title_full | Spinors in Five-Dimensional Contact Geometry |
| title_fullStr | Spinors in Five-Dimensional Contact Geometry |
| title_full_unstemmed | Spinors in Five-Dimensional Contact Geometry |
| title_short | Spinors in Five-Dimensional Contact Geometry |
| title_sort | spinors in five-dimensional contact geometry |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211637 |
| work_keys_str_mv | AT eastwoodmichael spinorsinfivedimensionalcontactgeometry AT moytimothy spinorsinfivedimensionalcontactgeometry |