Matter and Ricci Collineations

Abstract

The infinitesimal transformations that leave invariant a two-covariant symmetric tensor are studied. The interest of these symmetry transformations lies in the fact that this class of tensors includes the energy-momentum and Ricci tensors. Moreover, all curvature collineations are necessarily Ricci collineations. We find that in most cases the class of infinitesimal generators of these transformations is a finite dimensional Lie algebra but also, in some cases exhibiting a higher degree of degeneracy, this class is infinite dimensional and may fail to be a Lie algebra. © Springer-Verlag Berlin Heidelberg 2014.