Curvature-homogeneous pseudo-Riemannian Einstein four-manifolds

Abstract: In the Riemannian case they are all locally homogeneous (and hence locally symmetric due to a 1969 result of Jensen). By contrast, for the neutral sign pattern $(- - + +)$, simple examples show that the local-isometry types of curvature-homogeneous Ricci-flat metrics form an in finite-dimensional moduli space (and so "most" of them are not locally homogeneous). In the Lorentzian signature, the same phenomenon arises as a consequence of Brans's 1971 classification of Petrov type III metrics. The talk presents local-structure theorems for some special classes of such four-manifolds.

differential geometry

Audience: researchers in the topic

Workshop on compact homogeneous Einstein manifolds

Series comments: The workshop aims at bringing together mathematicians that have contributed and are contributing to the study of Einstein metrics on the challenging class of all compact homogeneous spaces.