Asymptotic symmetries of projectively compact order one Einstein manifolds

TL;DR

This paper investigates the boundary structure of projectively compact Einstein manifolds, revealing how their asymptotic symmetries can be understood through an extended boundary constructed via a natural line bundle.

Contribution

It introduces a novel boundary extension for projectively compact Einstein manifolds and links automorphisms of this boundary to asymptotic symmetries, based on a new curved orbit decomposition.

Findings

Boundary extension via a line bundle is possible for these manifolds.

Automorphisms of the extended boundary correspond to asymptotic symmetries.

A new curved orbit decomposition is established for the manifold.

Abstract

We show that the boundary of a projectively compact Einstein manifold of dimension $n$ can be extended by a line bundle naturally constructed from the projective compactification. This extended boundary is such that its automorphisms can be identified with asymptotic symmetries of the compactification. The construction is motivated by the investigation of a new curved orbit decomposition for a $n+1$ dimensional manifold which we prove results in a line bundle over a projectively compact order one Einstein manifolds.