Conformal structures with $G_{2(2)}$-ambient metrics
Differential Geometry
2012-08-14 v3
Abstract
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.
Keywords
Cite
@article{arxiv.0904.0186,
title = {Conformal structures with $G_{2(2)}$-ambient metrics},
author = {Thomas Leistner and Pawel Nurowski},
journal= {arXiv preprint arXiv:0904.0186},
year = {2012}
}
Comments
V3 is completely rewritten. We simplified all calculations by appropriately changing the metric in the conformal class. To make the paper more self contained, we avoid the use of tractor calculus. A gap in the proof that the ambient metric has holonomy equal to G_2 has been eliminated