Modified conformal extensions
| Authors | |
|---|---|
| Year of publication | 2023 |
| Type | Article in Periodical |
| Magazine / Source | Annals of Global Analysis and Geometry |
| MU Faculty or unit | |
| Citation | |
| Web | https://link.springer.com/article/10.1007/s10455-023-09918-9 |
| Doi | http://dx.doi.org/10.1007/s10455-023-09918-9 |
| Keywords | Differential geometry; Patterson-Walker metric; Projective structure; Conformal structure; Conformal Killing field; Einstein metric; Fefferman-Graham ambient metrics |
| Description | We present a geometric construction and characterization of 2n-dimensional split-signature conformal structures endowed with a twistor spinor with integrable kernel. The construction is regarded as a modification of the conformal Patterson-Walker metric construction for n-dimensional projective manifolds. The characterization is presented in terms of the twistor spinor and an integrability condition on the conformal Weyl curvature. We further derive a complete description of Einstein metrics and infinitesimal conformal symmetries in terms of suitable projective data. Finally, we obtain an explicit geometrically constructed Fefferman-Graham ambient metric and show the vanishing of the Q-curvature. |
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