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

TL;DR

This paper develops a method to construct canonical Carrollian geometries at infinity for projectively compact Ricci flat Einstein manifolds, linking projective structures to boundary geometries using a novel Cartan geometry approach.

Contribution

It introduces a new Cartan geometry framework based on a non-effective model to relate projective compactification data to Carrollian boundary geometries.

Findings

Constructed canonical Carrollian geometries at infinity.

Linked projective structures to boundary geometries.

Proved this structure is a general feature of such manifolds.

Abstract

In this article we discuss how to construct canonical \emph{strong} Carrollian geometries at time/space like infinity of projectively compact Ricci flat Einstein manifolds $(M,g)$ and discuss the 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.