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arXiv · 1501.00852

Explicit ambient metrics and holonomy

Ian M. Anderson·Thomas Leistner·Pawel Nurowski
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Abstract

We present three large classes of examples of conformal structures for which the equations for the Fefferman-Graham ambient metric to be Ricci-flat are linear PDEs, which we solve explicitly. These explicit solutions enable us to discuss the holonomy of the corresponding ambient metrics. Our examples include conformal pp-waves and, more importantly, conformal structures that are defined by generic rank 2 and 3 distributions in respective dimensions 5 and 6. The corresponding explicit Fefferman-Graham ambient metrics provide a large class of metrics with holonomy equal to the exceptional non-compact Lie group $\mathbf{G}_2$ as well as ambient metrics with holonomy contained in $\mathbf{Spin}(4,3)$.

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Ian M. Anderson, Thomas Leistner, Pawel Nurowski. 2015-01-05. Explicit ambient metrics and holonomy. https://doi.org/10.4310/jdg%2F1580526015

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