Document Type

Article

Journal/Book Title/Conference

Journal of Differential Geometry

Volume

114

Issue

2

Publisher

Lehigh University Department of Mathematics

Publication Date

2-1-2020

First Page

1

Last Page

52

Abstract

We present three large classes of examples of conformal structures whose Fefferman-Graham ambient metrics can be found explicitly. Our method for constructing these examples rests upon a set of sufficiency conditions under which the Fefferman-Graham equations are assured to reduce to a system of inhomogeneous linear partial differential equations. Our examples include conformal pp-waves and, more importantly, conformal structures that are defined by generic co-rank 3 distributions in dimensions 5 and 6.Our examples illustrate various aspects of the ambient metric construction.

The holonomy algebras of our ambient metrics are studied in detail. In particular, we exhibit a large class of metrics with holonomy equal to the exceptional non-compact Lie group G2 as well as ambient metrics with holonomy contained in Spin(4, 3).

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