SPACE-TIMES WITH A 2-DIMENSIONAL GROUP OF CONFORMAL MOTIONS

The necessary and sufficient conditions for a space-time to admit a tw o-dimensional group of conformal motions (and, in particular, of homot hetic motions) acting on nonnull orbits are found in the compacted spi n-coefficient formalism. Although the discussion is restricted to the case of spacelike orbits, similar results are readily obtained for tim elike orbits via the (modified) Sachs star operation. A number of theo rems are obtained dealing with such topics as the Gaussian curvature o f the group orbits, orthogonal transitivity, and hypersurface orthogon ality of the conformal Killing vectors. A simple proof is presented of a generalization of a theorem due to Papapetrou.