Rigidité infinitésimale de cônes-variétés Einstein à courbure négative.

Grégoire Montcouquiol (1)

1 LEP - Laboratoire Émile Picard

Starting with a compact hyperbolic cone-manifold of dimension greater than or equal to 3, we study the deformations of the metric with the aim of getting Einstein cone-manifolds. If the singular locus is a closed codimension 2 submanifold and all cone angles are smaller than 2 pi, we show that there is no non-trivial infinitesimal Einstein deformations preserving the cone angles.

Mots clés: cone-manifolds; Einstein metrics; infinitesimal rigidity

Domaines: Géométrie différentielle [math.DG]

Grégoire Montcouquiol. Rigidité infinitésimale de cônes-variétés Einstein à courbure négative.. 2005. ⟨hal-00004415⟩