9/16/2011

Robin Graham
University of Washington

Ambient metrics and exceptional holonomy

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 $G_2$.  An open dense subset of the family has holonomy equal to $G_2$.  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.