Conformal structures with explicit ambient metrics and conformal G₂ holonomy

2007/01/30 by Paweł Nurowski, Nurowski, Pawel · 1 citation
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.math/0701891

openalex publication_date 2007/01/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 G₂. 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 G₂-holonomy of metrics [g] and the possible pseudo-Riemannian G₂-holonomy of the corresponding ambient metrics.

Cited by

• Geometric aspects of rank-3 vector bundles over surfaces and 2-plane distributions on 5-manifolds

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