涩里番

Title: Examples of Compact Einstein four-manifolds with negative curvature.

Abstract: We construct new examples of closed, negatively curved Einstein four-manifolds. More precisely, we construct听 Einstein metrics of negative sectional curvature on ramified covers of compact hyperbolic four-manifolds with symmetries, initially considered by Gromov and Thurston. These metrics are obtained through a deformation procedure.听 Our candidate approximate Einstein metric is an interpolation between a black-hole Riemannian Einstein metric near the branch locus and the pulled-back hyperbolic metric. We then deform it into a genuine solution of Einstein鈥檚 equations, and the deformation relies on an involved bootstrap procedure. Our construction yields the first example of compact Einstein manifolds with negative sectional curvature which are not locally homogeneous. This is a joint听 work with J. Fine (ULB, Brussels).

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