Affine and projective symmetry in general relativity
A result regarding the decomposition of space-time using the Reimann tensor is proved and applied to other decompositions, as well as to the study of projective symmetry. Affine and homothetic symmetries, including the zeros of proper homothetic vector fields and the orbit structure of affine, homothetic and Killing symmetries are also studied, and a link to plane wave space-times established. Projective symmetry is investigated in conformally flat perfect fluid space-times, whilst the non-existence of proper projective symmetry in certain space-times is proved. The form of the Killing vector fields in a constant curvature manifold of arbitrary dimension and arbitrary metric signature is derived.