Abstract
The necessary and sufficient conditions for a space–time to admit a two-dimensional group of conformal motions (and, in particular, of homothetic motions) acting on nonnull orbits are found in the compacted spin-coefficient formalism. Although the discussion is restricted to the case of spacelike orbits, similar results are readily obtained for timelike orbits via the (modified) Sachs star operation. A number of theorems are obtained dealing with such topics as the Gaussian curvature of the group orbits, orthogonal transitivity, and hypersurface orthogonality of the conformal Killing vectors. A simple proof is presented of a generalization of a theorem due to Papapetrou.
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