Apparaît dans la collection : Summer School 2014 - Asymptotic Analysis in General Relativity

Conformal compactification has long been recognised as an effective geometric framework for relating conformal geometry, and associated field theories « at infinity », to the asymptotic phenomena of an interior (pseudo­‐)­‐Riemannian geometry of one higher dimension. It provides an effective approach for analytic problems in GR, geometric scattering, conformal invariant theory, as well as the AdS/CFT correspondence of Physics. I will describe how the notion of conformal compactification can be linked to Cartan holonomy reduction. This leads to a conceptual way to define other notions of geometric compactification. The idea will be taken up, in particular, for the case of compactifying pseudo‐Riemannian manifolds using projective geometry. A new characterisation of projectively compact metrics will be given, and some results on their asymptotics near the conformal infinity. This is joint work with Andreas Cap.