Geometric structures, compactifications and group actions

Résumé

Every Lorentzian manifold (M, g) has a natural projective structure induced by its Levi- Civita connection. In some cases, M can be embedded into a manifold with boundary M, in which the projective structure extends to the boundary: (M, g) is then said to be projectively compact. In this talk, we will discuss applications of the projective structure to the asymptotic analysis of partial differential equations, in particular a generalised Proca equation, on projectively compact Lorentzian manifolds.