Curvature collineation

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

• Conformal vector field
• Homothetic vector field
• Killing vector field
• Matter collineation
• Spacetime symmetries