Article Dans Une Revue Geometriae Dedicata Année : 2025

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 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.

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hal-04605759 , version 1 (10-06-2025)

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Jack Borthwick, Yannick Herfray. Projective and Carrollian geometry at time/space-like infinity on projectively compact Ricci flat Einstein manifolds. Geometriae Dedicata, 2025, 219 (1), pp.12. ⟨10.1007/s10711-024-00973-5⟩. ⟨hal-04605759⟩
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