Conformal structures with explicit ambient metrics and conformal G_2 holonomy
摘要
Given a generic 2-plane field on a 5-dimensional manifold we consider its (3,2)-signature conformal metric [g] as defined in math.DG/0406400. Every conformal class [g] obtained in this way has very special conformal holonomy: it must be contained in the split-real-form of the exceptional group G_2. In this note we show that for special 2-plane fields on 5-manifolds the conformal classes [g] have the Fefferman-Graham ambient metrics which, contrary to the general Fefferman-Graham metrics given as a formal power series, can be written in an explicit form. We propose to study the relations between the conformal G_2-holonomy of metrics [g] and the possible pseudo-Riemannian G_2-holonomy of the corresponding ambient metrics.
引用
@article{arxiv.math/0701891,
title = {Conformal structures with explicit ambient metrics and conformal G_2 holonomy},
author = {Pawel Nurowski},
journal= {arXiv preprint arXiv:math/0701891},
year = {2007}
}
备注
To appear in Proceedings of the Workshop at 2006 IMA Summer Program "Symmetries and Overdetermined Systems of Partial Differential Equations", Minneapolis, July 2006