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This article is cited in 3 scientific papers (total in 3 papers)
A Projective-to-Conformal Fefferman-Type Construction
Matthias Hammerla, Katja Sagerschnigb, Josef Šilhanc, Arman Taghavi-Chabertd, Vojtěch Žádníke a University of Vienna, Faculty of Mathematics, Oskar-Morgenstern-Platz 1, 1010 Vienna, Austria
b INdAM-Politecnico di Torino, Dipartimento di Scienze Matematiche, Corso Duca degli Abruzzi 24, 10129 Torino, Italy
c Masaryk University, Faculty of Science, Kotlářská 2, 61137 Brno, Czech Republic
d Università di Torino, Dipartimento di Matematica ''G. Peano'', Via Carlo Alberto 10, 10123 Torino, Italy
e Masaryk University, Faculty of Education, Poříčí 31, 60300 Brno, Czech Republic
Abstract:
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.
Received: February 9, 2017; in final form October 9, 2017; Published online October 21, 2017
Citation:
Matthias Hammerl, Katja Sagerschnig, Josef Šilhan, Arman Taghavi-Chabert, Vojtěch Žádník, “A Projective-to-Conformal Fefferman-Type Construction”, SIGMA, 13 (2017), 081, 33 pp.
Linking options:
https://www.mathnet.ru/eng/sigma1281 https://www.mathnet.ru/eng/sigma/v13/p81
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