Curvature collineation
A curvature collineation (often abbreviated to CC) is vector field which preserves the Riemann tensor in the sense that, L X R a b c d = 0 {\displaystyle {\mathcal {L}}_{X}R^{a}{}_{bcd}=0} where R a b c d {\displaystyle R^{a}{}_{bcd}} are the components of the Riemann tensor. The set of all smooth curvature collineations forms a Lie algebra under the Lie bracket operation (if the smoothness condition is dropped, the set of all curvature collineations need not form a Lie algebra).