Glueing constructions of Compact Einstein four-manifolds with negative sectional

Abstract: We construct examples of closed Einstein four-manifolds with negative sectional curvature. We describe two main families of examples which are respectively obtained as ramified covers and smooth quotients of ``large’’ hyperbolic 4-manifolds with symmetries. The first family of examples is sometimes referred to as Gromov-Thurston manifolds. The Einstein metrics that we construct are the result of a glueing procedure. They are obtained as deformations of an approximate Einstein metric which is an interpolation between a ``black-hole – type’’ Riemannian Einstein metric near the symmetry locus and the hyperbolic metric. This construction yields the first example of compact Einstein manifolds with negative sectional curvature which are not locally homogeneous. This is a joint work with J. Fine (ULB, Brussels).

differential geometry

Audience: researchers in the topic

Pangolin seminar

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