Explicit ambient metrics and holonomy

Date & time

11.45am–12.45pm 12 March 2015


Building 27, Room G35


Professor Thomas Leistner (University of Adelaide)


 Dennis The

I will report on recent work with I. Anderson and P. Nurowski in which we present three classes of conformal structures for which the equations for the Fefferman-Graham ambient metric to be Ricci-flat are linear PDEs, which we solve explicitly. These explicit solutions enable us to discuss the holonomy of the corresponding ambient metrics. Our examples include conformal pp-waves and, more importantly, conformal structures that are defined by generic rank 2 and 3 distributions in respective dimensions 5 and 6. The corresponding explicit Fefferman-Graham ambient metrics provide a class of metrics with holonomy equal to the exceptional non-compact Lie group G_2 as well as ambient metrics with holonomy contained in Spin(4,3).

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