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Article
Explicit Ambient Metrics and Holonomy
Journal of Differential Geometry
  • Ian M. Anderson, Utah State University
  • Thomas Leistner, University of Adelaide
  • Pawel Nurowski, Centrum Fizyki Teoretycznej PAN
Document Type
Article
Publisher
Lehigh University Department of Mathematics
Publication Date
2-1-2020
Disciplines
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).

Citation Information
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