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arXiv · 1604.08471

Conformal Patterson-Walker metrics

Matthias Hammerl·Katja Sagerschnig·Josef Šilhan·Arman Taghavi-Chabert·Vojtěch Žádník
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Abstract

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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Matthias Hammerl, Katja Sagerschnig, Josef Šilhan, Arman Taghavi-Chabert, Vojtěch Žádník. 2020-08-27. Conformal Patterson-Walker metrics. https://doi.org/10.4310/ajm.2019.v23.n5.a1

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