Compact Einstein-Weyl manifolds with large symmetry group
The authors give a classification of 4-dimensional compact Einstein-Weyl manifolds whose symmetry group is at least 4-dimensional. A Weyl geometry consists of a conformal class \([g]\) of metrics and a connection \(D\) such that for all \(g\in [g]\) there exists a 1-form \(\omega\) with \(Dg= \omega \otimes g\). From reading the proof of Lemma 2.2 it seems that the authors restrict their consideration to positive signature \((+,+,+,+)\). An Einstein-Weyl manifold is a Weyl geometry such that \(Sr^D= \Lambda g\), where \(Sr^D\) is the symmetrization of the Ricci tensor and \(\Lambda\) is a constant.
scientific article; zbMATH DE number 1042490
scientific article