Conformal Patterson-Walker metrics

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Authors

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

Year of publication 2019
Type Article in Periodical
Magazine / Source The Asian Journal of Mathematics
MU Faculty or unit

Faculty of Science

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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