Séminaire de Géométrie

Exemples de variétés d'Einstein compactes de dimension 4 à courbure négative

by Mr Bruno Premoselli (Université Libre de Bruxelles)

1180 (Bât E2)


Bât E2

Site Grandmont

We construct new examples of closed, negatively curved, not locally homogeneous Einstein four-manifolds. Topologically, the manifolds we consider are of two types: quotients by the action of a dihedral group of symmetric closed hyperbolic four-manifolds on the one hand, and ramified covers over hyperbolic manifolds with symmetries on the other hand. We produce an Einstein metric on such manifolds via a glueing procedure. We first find an approximate Einstein metric that we obtain as the interpolation, at large distances, between a Riemannian Kottler metric and the hyperbolic metric. We then deform it, in the Bianchi gauge, into a genuine solution of Einstein’s equations. The constructions described in this talk are a joint work with J. Fine (ULB).