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@article{1399439,
author = {Hammerl, Matthias and Sagerschnig, Katja and Šilhan, Josef and TaghaviandChabert, Arman and Žádník, Vojtěch},
article_number = {81},
doi = {http://dx.doi.org/10.3842/SIGMA.2017.081},
keywords = {parabolic geometry; projective structure; conformal structure; Cartan connection; Fefferman spaces; twistor spinors},
language = {eng},
issn = {1815-0659},
journal = {Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)},
title = {A Projective-to-Conformal Fefferman-Type Construction},
url = {https://www.emis.de/journals/SIGMA/2017/081/},
volume = {13},
year = {2017}
}
TY - JOUR
ID - 1399439
AU - Hammerl, Matthias - Sagerschnig, Katja - Šilhan, Josef - Taghavi-Chabert, Arman - Žádník, Vojtěch
PY - 2017
TI - A Projective-to-Conformal Fefferman-Type Construction
JF - Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
VL - 13
IS - 81
SP - 1-33
EP - 1-33
SN - 18150659
KW - parabolic geometry
KW - projective structure
KW - conformal structure
KW - Cartan connection
KW - Fefferman spaces
KW - twistor spinors
UR - https://www.emis.de/journals/SIGMA/2017/081/
L2 - https://www.emis.de/journals/SIGMA/2017/081/
N2 - 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.
ER -
HAMMERL, Matthias, Katja SAGERSCHNIG, Josef ŠILHAN, Arman TAGHAVI-CHABERT a Vojtěch ŽÁDNÍK. A Projective-to-Conformal Fefferman-Type Construction. \textit{Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)}. roč.~13, č.~81, s.~1-33. ISSN~1815-0659. doi:10.3842/SIGMA.2017.081. 2017.
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