A Projective-to-Conformal Fefferman-Type Construction
| Authors | |
|---|---|
| Year of publication | 2017 |
| Type | Article in Periodical |
| Magazine / Source | Symmetry, Integrability and Geometry: Methods and Applications (SIGMA) |
| MU Faculty or unit | |
| 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. |
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