Publication details
Conformal Patterson-Walker metrics
| Authors | |
|---|---|
| Year of publication | 2019 |
| Type | Article in Periodical |
| Magazine / Source | The Asian Journal of Mathematics |
| MU Faculty or unit | |
| Citation | |
| Web | https://www.intlpress.com/site/pub/pages/journals/items/ajm/content/vols/0023/0005/a001/index.php |
| Doi | http://dx.doi.org/10.4310/AJM.2019.v23.n5.a1 |
| Keywords | Differential geometry; Parabolic geometry; Projective structure; Conformal structure; Einstein metrics; Conformal Killing field; Twistor spinors |
| Description | The classical Patterson-Walker construction of a split-signature (pseudo-)Riemannian structure from a given torsion-free affine connection is generalized to a construction of a split-signature conformal structure from a given projective class of connections. A characterization of the induced structures is obtained. We achieve a complete description of Einstein metrics in the conformal class formed by the Patterson-Walker metric. Finally, we describe all symmetries of the conformal Patterson-Walker metric. In both cases we obtain descriptions in terms of geometric data on the original structure. |
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