We construct 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.
The approximate Einstein metric is an interpolation between a black‐hole Einstein metric near the branch locus and the pulled‐back hyperbolic metric. 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 work with J. Fine (ULB).
Bruno Premoselli (UL Brussels): Examples of Compact Einstein four‐manifolds with negative curvature
Location:
Verwandte Dateien
Foto: Barbara Mair