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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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2017 |
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| Language: | English |
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Інститут математики НАН України
2017
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/149272 |
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| Cite this: | 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. |
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Hammerl, M. Sagerschnig, K. Šilhan, J. Taghavi-Chabert, A. Zádník, V. 2019-02-19T19:38:06Z 2019-02-19T19:38:06Z 2017 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 https://nasplib.isofts.kiev.ua/handle/123456789/149272 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. The authors express special thanks to Maciej Dunajski for motivating the study of this construction and for a number of enlightening discussions on this and adjacent topics. KS would also like to thank Pawe l Nurowski for drawing her interest to the subject and for many useful conversations. MH gratefully acknowledges support by project P23244-N13 of the Austrian Science Fund (FWF) and by ‘Forschungsnetzwerk Ost’ of the University of Greifswald. KS gratefully acknowledges support from grant J3071-N13 of the Austrian Science Fund (FWF). JS was supported ˇ by the Czech science foundation (GACR) under grant P201/12/G028. AT-C was funded by ˇ GACR post-doctoral grant GP14-27885P. V ˇ Z was supported by GA ˇ CR grant GA201/08/0397. ˇ Finally, the authors would like to thank the anonymous referees for their helpful comments and recommendations. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications A Projective-to-Conformal Fefferman-Type Construction Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
A Projective-to-Conformal Fefferman-Type Construction |
| spellingShingle |
A Projective-to-Conformal Fefferman-Type Construction Hammerl, M. Sagerschnig, K. Šilhan, J. Taghavi-Chabert, A. Zádník, V. |
| 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 |
| author |
Hammerl, M. Sagerschnig, K. Šilhan, J. Taghavi-Chabert, A. Zádník, V. |
| author_facet |
Hammerl, M. Sagerschnig, K. Šilhan, J. Taghavi-Chabert, A. Zádník, V. |
| publishDate |
2017 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| 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.
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/149272 |
| citation_txt |
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. |
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2025-12-07T18:56:32Z |
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