Curvature Symmetry
A curvature collineation is a vector field which preserves the Riemann tensor:
where 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). The Lie algebra is denoted by and may be infinite-dimensional. Every affine vector field is a curvature collineation.
Read more about this topic: Spacetime Symmetries
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—George Gordon Noel Byron (1788–1824)