Projective and Carrollian geometry at time/space-like infinity on projectively compact Ricci flat Einstein manifolds - Archive ouverte HAL Access content directly
Preprints, Working Papers, ... Year : 2024

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

Abstract

In this article we discuss how to construct canonical 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.

Dates and versions

hal-04605759 , version 1 (08-06-2024)

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Jack Borthwick, Yannick Herfray. Projective and Carrollian geometry at time/space-like infinity on projectively compact Ricci flat Einstein manifolds. 2024. ⟨hal-04605759⟩
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