On some family of generalized Einstein metric conditions (Q2777568)

The authors continue their study of the so-called pseudosymmetry conditions on semi-Riemannian manifolds. The work is motivated by the fact, proven in the paper, that a semi-Riemannian Einstein space of dimension \(\geq 4\) satisfies a particular type of pseudosymmetry relating the curvature tensor \(R\) and the Weyl tensor \(C\). This relation is called a generalized Einstein metric condition. Then they make a detailed study of this condition for manifolds which are not Einsteinian and not conformally flat and focus on relations with other types of pseudosymmetry.