A Projective-to-Conformal Fefferman-Type Construction
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
A Projective-to-Conformal Fefferman-Type Construction
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| Creator |
Hammerl, M.
Sagerschnig, K. Šilhan, J. Taghavi-Chabert, A. Zádník, V. |
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| 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.
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| Date |
2019-02-19T19:38:06Z
2019-02-19T19:38:06Z 2017 |
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| Type |
Article
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| Identifier |
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 |
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| Language |
en
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| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
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| Publisher |
Інститут математики НАН України
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