HAMMERL, Matthias, Katja SAGERSCHNIG, Josef ŠILHAN, Arman TAGHAVI-CHABERT a Vojtěch ŽÁDNÍK. A Projective-to-Conformal Fefferman-Type Construction. Symmetry, Integrability and Geometry: Methods and Applications (SIGMA). 2017, roč. 13, č. 81, s. 1-33. ISSN 1815-0659. Dostupné z: https://dx.doi.org/10.3842/SIGMA.2017.081. |
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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)}. 2017, roč.~13, č.~81, s.~1-33. ISSN~1815-0659. Dostupné z: https://dx.doi.org/10.3842/SIGMA.2017.081.
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