Curvature-homogeneous indefinite Einstein metrics in dimension four: the diagonalizable case
Curvature-homogeneous indefinite Einstein metrics in dimension four: the diagonalizable case
We classify those curvature-homogeneous Einstein four-manifolds, of all metric signatures, which have a complex-diagonalizable curvature operator. They all turn out to be locally homogeneous. More precisely, any such manifold must be either locally symmetric or locally isometric to a suitable Lie group with a left-invariant metric. To show this we …