标题： 在投影紧致的零曲率爱因斯坦流形的时间/类空无限远处的射影几何和卡罗尔几何 显示英文标题

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

摘要： 在本文中，我们讨论如何构造规范的\emph{强}卡罗尔几何，在射影紧致的里奇平坦爱因斯坦流形$(M,g)$的时间/空间无限远处，并讨论该度量的底层射影结构之间的联系$g$。 获得的卡罗尔几何由射影紧致化的数据确定。 实现这一目标的关键思想是考虑一种基于射影几何非有效齐次模型的新类型的卡坦几何。 我们证明这种结构是射影紧致的里奇平坦爱因斯坦流形的一个普遍特征。 显示英文摘要

摘要： 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.