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

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.

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

References in corpus (4)

• Ambient metrics for $n$-dimensional $pp$-waves
• Normal Conformal Killing Forms
• Conformal Structures Associated to Generic Rank 2 Distributions on 5-Manifolds - Characterization and Killing-Field Decomposition
• A sub-product construction of Poincare-Einstein metrics

Cited by in corpus (7)

• Conformal Structures Associated to Generic Rank 2 Distributions on 5-Manifolds - Characterization and Killing-Field Decomposition
• The twistor spinors of generic 2- and 3-distributions
• Nearly Kähler Geometry and $(2,3,5)$-Distributions via Projective Holonomy
• The Geometry of Almost Einstein (2,3,5) Distributions
• Parallel tractor extension and ambient metrics of holonomy split G_2
• Conformal superalgebras via tractor calculus
• Homogeneous Real (2,3,5) Distributions with Isotropy