Journal of Differential Geometry
Lehigh University Department of Mathematics
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).
Anderson, Ian M.; Leistner, Thomas; Nurowski, Paweł. Explicit ambient metrics and holonomy. J. Differential Geom. 114 (2020), no. 2, 193--242. doi:10.4310/jdg/1580526015. https://projecteuclid.org/euclid.jdg/1580526015