Séminaire de Physique Théorique

Projective differential geometry and asymptotic analysis in General Relativity

by Dr Jack Borthwick (Université de Franche-Comté)

salle 1180 (IDP Tours)

salle 1180

IDP Tours

Institut Denis Poisson Université de Tours Facultés des Sciences et Techniques Bâtiment E2, Parc de Grandmont 37200 Tours FRANCE

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 {\bar 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 generalized Proca equation, on projectively compact Lorentzian manifolds.