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A Projective-to-Conformal Fefferman-Type Construction
Symmetry, integrability and geometry: methods and applications, Tome 13 (2017) Cet article a éte moissonné depuis la source Math-Net.Ru

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We study a Fefferman-type construction based on the inclusion of Lie groups ${\rm SL}(n+1)$ into ${\rm Spin}(n+1,n+1)$. 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.
Keywords: parabolic geometry; projective structure; conformal structure; Cartan connection; Fefferman spaces; twistor spinors. 
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     author = {Matthias Hammerl and Katja Sagerschnig and Josef \v{S}ilhan and Arman Taghavi-Chabert and Vojt\v{e}ch \v{Z}\'adn{\'\i}k},
     title = {A {Projective-to-Conformal} {Fefferman-Type} {Construction}},
     journal = {Symmetry, integrability and geometry: methods and applications},
     year = {2017},
     volume = {13},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2017_13_a80/}
}
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Matthias Hammerl; Katja Sagerschnig; Josef Šilhan; Arman Taghavi-Chabert; Vojtěch Žádník. A Projective-to-Conformal Fefferman-Type Construction. Symmetry, integrability and geometry: methods and applications, Tome 13 (2017). http://geodesic.mathdoc.fr/item/SIGMA_2017_13_a80/

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