Projective and Carrollian geometry at time/space-like infinity on projectively compact Ricci flat Einstein manifolds

Résumé

In this article we discuss how to construct canonical strong Carrollian geometries at time/space-like infinity of projectively compact Ricci flat Einstein manioflds $(M,g)$ and discuss links between the underlying projective structure of the metric $g$. The obtained Carrollian geometries are determined by the data of the projective compactification. The key idea to achieve this is to consider a new type of Cartan geometry based on a non-effective homogeneous model for projective geometry. We prove that this structure is a general feature of projectively compact Ricci flat Einstein manifolds.