Conformal structures with $G_{2(2)}$-ambient metrics

Thomas Leistner, Pawel Nurowski

Published 2009-04-01, updated 2010-03-05Version 3

We present conformal structures in signature (3,2) for which the holonomy of the Fefferman-Graham ambient metric is equal to the non-compact exceptional Lie group G_{2(2)}. We write down the resulting 8-parameter family of G_{2(2)}-metrics in dimension seven explicitly in an appropriately chosen coordinate system on the ambient space.