Curvature collineation explained
A curvature collineation (often abbreviated to CC) is vector field which preserves the Riemann tensor in the sense that,
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.
See also
