Séminaire de Physique ThéoriqueFefferman-Graham metrics as solutions to linear PDEs.
Pawel Nurowski (Centre de Physique Théorique, Varsovie)
Monday 12 March 2018 11:00 - Tours - Salle 1180 (Bât E2)
I will present three classes of examples of conformal structures for which the equations for the Fefferman-Graham ambient metric to be Ricci-flat are linear PDEs. These permits to write down Fefferman-Graham metrics in explicit forms, which I will use to discuss the holonomy of the 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 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).