| Résume | We construct new examples of closed, negatively curved, not locally homogeneous Einstein four-manifolds. Topologically, the manifolds we consider are quotients, by the action of a dihedral group, of symmetric closed hyperbolic four-manifolds. 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 construction described in this talk is a joint work with J. Fine (ULB) and is inspired from our recent construction of Einstein metrics on ramified covers of closed hyperbolic manifolds with symmetries. |
