Ambient metrics and exceptional holonomy

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Robin Graham, University of Washington

Construction of pseudo-Riemannian metrics whose holonomy is an exceptional Lie group has been of interest in recent years.  This talk will outline a construction of an infinite-dimensional family of metrics in dimension 7 whose holonomy is contained in the split real form of the exceptional group G2.  An open dense subset of the family has holonomy equal to G2.  The datum for the construction is a generic real-analytic 2-plane field on a manifold of dimension 5; the metric in dimension 7 arises as the ambient metric of a conformal structure on the 5-manifold defined by Nurowski in terms of the 2-plane field.This is work with Travis Willse and generalizes results of Leistner and Nurowski.