Séance Séminaire

Séminaire Gaston Darboux

Projective background of (2+1)-spacetimes of constant curvature

William Thurston in his Geometrization Program suggested a new approach to locally homogeneous Riemannian structures and highlighted their significance for 3-dimensional topology. It was soon recognized that Thurston's approach is also very fruitful in non-Riemannian settings, particularly in Lorentzian, as it was demonstrated by the pioneering work of Geoffrey Mess on (2+1)-spacetimes of constant curvature. Geometries of constant curvature, whether Riemannian or Lorentzian, can be considered as subgeometries of projective geometry, which in particular allows to perform interesting geometric transitions between different geometries. In my talk I will describe how this viewpoint allows to deduce rigidity results on anti-de Sitter (2+1)-spacetimes using the resolution of analogous problems in the setting of Minkowski spacetimes. The talk is partially based on joint works with François Fillastre and Jean-Marc Schlenker.