Curvature properties of some four-dimensional manifolds (Q2777565)

In [Differ. Geom. Appl. 10, No. 3, 257-294 (1999; Zbl 0921.53006)] \textit{M. A. Akivis} and \textit{V. V. Goldberg} made a detailed study of manifolds \(M\) equipped with an almost Grassmann structure \(AG(p-1, p+q-1)\), \(\dim M= pq\), defined by means of a fibration of Segre cones \(SC(p,q)\). When \(\dim M=4\), such an almost Grassmann structure is of type \(A(1,3)\) and is equivalent with a pseudoconformal structure \(CO(2,2)\). In the same paper, several explicit examples of four-dimensional semi-Riemannian manifolds with such a structure are given. NEWLINENEWLINENEWLINEIn the paper under review, the author focusses on the study of a list of curvature properties for these examples, in particular curvature properties of pseudosymmetry type as introduced and studied by R. Deszcz and his group of collaborators.