A Projective-to-Conformal Fefferman-Type Construction
We study a Fefferman-type construction based on the inclusion of Lie groups SL(n+1) into Spin(n+1,n+1). The construction associates a split-signature (n,n)-conformal spin structure to a projective structure of dimension n. We prove the existence of a canonical pure twistor spinor and a light-like co...
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| Дата: | 2017 |
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| Автори: | , , , , |
| Формат: | Стаття |
| Мова: | English |
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Інститут математики НАН України
2017
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/149272 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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irk-123456789-1492722019-02-20T01:23:44Z A Projective-to-Conformal Fefferman-Type Construction Hammerl, M. Sagerschnig, K. Šilhan, J. Taghavi-Chabert, A. Zádník, V. We study a Fefferman-type construction based on the inclusion of Lie groups SL(n+1) into Spin(n+1,n+1). The construction associates a split-signature (n,n)-conformal spin structure to a projective structure of dimension n. We prove the existence of a canonical pure twistor spinor and a light-like conformal Killing field on the constructed conformal space. We obtain a complete characterisation of the constructed conformal spaces in terms of these solutions to overdetermined equations and an integrability condition on the Weyl curvature. The Fefferman-type construction presented here can be understood as an alternative approach to study a conformal version of classical Patterson-Walker metrics as discussed in recent works by Dunajski-Tod and by the authors. The present work therefore gives a complete exposition of conformal Patterson-Walker metrics from the viewpoint of parabolic geometry. 2017 Article A Projective-to-Conformal Fefferman-Type Construction / M. Hammerl, K. Sagerschnig, J. Šilhan, A. Taghavi-Chabert, V. Zádník// Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 30 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 53A20; 53A30; 53B30; 53C07 DOI:10.3842/SIGMA.2017.081 http://dspace.nbuv.gov.ua/handle/123456789/149272 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
We study a Fefferman-type construction based on the inclusion of Lie groups SL(n+1) into Spin(n+1,n+1). The construction associates a split-signature (n,n)-conformal spin structure to a projective structure of dimension n. We prove the existence of a canonical pure twistor spinor and a light-like conformal Killing field on the constructed conformal space. We obtain a complete characterisation of the constructed conformal spaces in terms of these solutions to overdetermined equations and an integrability condition on the Weyl curvature. The Fefferman-type construction presented here can be understood as an alternative approach to study a conformal version of classical Patterson-Walker metrics as discussed in recent works by Dunajski-Tod and by the authors. The present work therefore gives a complete exposition of conformal Patterson-Walker metrics from the viewpoint of parabolic geometry. |
| format |
Article |
| author |
Hammerl, M. Sagerschnig, K. Šilhan, J. Taghavi-Chabert, A. Zádník, V. |
| spellingShingle |
Hammerl, M. Sagerschnig, K. Šilhan, J. Taghavi-Chabert, A. Zádník, V. A Projective-to-Conformal Fefferman-Type Construction Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Hammerl, M. Sagerschnig, K. Šilhan, J. Taghavi-Chabert, A. Zádník, V. |
| author_sort |
Hammerl, M. |
| title |
A Projective-to-Conformal Fefferman-Type Construction |
| title_short |
A Projective-to-Conformal Fefferman-Type Construction |
| title_full |
A Projective-to-Conformal Fefferman-Type Construction |
| title_fullStr |
A Projective-to-Conformal Fefferman-Type Construction |
| title_full_unstemmed |
A Projective-to-Conformal Fefferman-Type Construction |
| title_sort |
projective-to-conformal fefferman-type construction |
| publisher |
Інститут математики НАН України |
| publishDate |
2017 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/149272 |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
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2023-05-20T17:31:27Z |
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