Pseudosymmetry collineations

Abstract

The pseudosymmetric spaces are a generalization of the spaces of constant sectional curvature in the sense that a scalar-valued curvature function, now depending on two planes, is assumed to be isotropic. From the study of the pseudosymmetry condition, a new set of tensors on the manifold receives attention and an invariance group on this set of tensors is introduced, the so-called pseudosymmetry collineations. This group is the infinitesimal counterpart of the pseudosymmetry condition. Their relationship with other types of transformations is discussed and, as an example, the pseudosymmetry collineations for the vacuum pp-waves are explicitly obtained.