A Projective-to-Conformal Fefferman-Type Construction

Investor logo
Investor logo
Investor logo

Warning

This publication doesn't include Faculty of Education. It includes Faculty of Science. Official publication website can be found on muni.cz.

Authors

HAMMERL Matthias SAGERSCHNIG Katja ŠILHAN Josef TAGHAVI-CHABERT Arman ŽÁDNÍK Vojtěch

Year of publication 2017
Type Article in Periodical
Magazine / Source Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
MU Faculty or unit

Faculty of Science

Citation
Web https://www.emis.de/journals/SIGMA/2017/081/
Doi http://dx.doi.org/10.3842/SIGMA.2017.081
Field General mathematics
Keywords parabolic geometry; projective structure; conformal structure; Cartan connection; Fefferman spaces; twistor spinors
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.
Related projects:

You are running an old browser version. We recommend updating your browser to its latest version.