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arXiv · 1608.06875

Fefferman-Graham ambient metrics of Patterson-Walker metrics

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

Given an $n$-dimensional manifold $N$ with an affine connection $D$, we show that the associated Patterson-Walker metric $g$ on $T^*N$ admits a global and explicit Fefferman-Graham ambient metric. This provides a new and large class of conformal structures which are generically not conformally Einstein but for which the ambient metric exists to all orders and can be realized in a natural and explicit way. In particular, it follows that Patterson-Walker metrics have vanishing Fefferman-Graham obstruction tensors. As an application of the concrete ambient metric realization we show in addition that Patterson-Walker metrics have vanishing Q-curvature.

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Matthias Hammerl, Katja Sagerschnig, Josef Šilhan, Arman Taghavi-Chabert, Vojtěch Žádník. 2016-08-24. Fefferman-Graham ambient metrics of Patterson-Walker metrics. https://doi.org/10.1112/blms.12136

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