Invariant Ricci collineations on three-dimensional Lie groups

Abstract

a b s t r a c tWe determine all left-invariant Ricci collineations on three-dimensional Lie groups.

On the symmetries of Siklos spacetimes

“…We may refer to [15] for a thorough survey and further information on symmetries. Examples of investigations of Ricci collineations in some classes of Lorentzian manifolds may be found in [9,10,13,[16][17][18][19][20]31] and references therein.…”

On symmetries of the Heisenberg group

“…Since symmetries are more significant from physical aspects, symmetries were studied on several kinds of space-times (see [1,4,5,2,3] and references therein). Symmetry analysis of the Heisenberg groups, which arise in the mathematical description of one-dimensional quantum mechanical systems, are the subject of the present research.…”

Symmetries of Lorentzian Three-Manifolds with Recurrent Curvature

“…We may refer to the monograph [16] for further information and references on symmetries. Ricci and curvature collineations have been investigated in several classes of Lorentzian manifolds (see, for example, [1,6,7,8,9,13,15,17,18,19,20,21,22] and references therein). Because of their physical relevance, in most cases curvature symmetries have been studied for some spacetimes.…”

“…Because of their physical relevance, in most cases curvature symmetries have been studied for some spacetimes. Moreover, the three-dimensional case has also been considered as an interesting source of examples and different behaviours (see, for example, [8]).…”