Classification and conformal symmetry in three-dimensional space-times

Three-dimensional manifolds admitting Lorentz metrics are studied. The first part of the paper gives a classification of the Ricci and curvature tensors and also of the conformal (Schouten-Cotton-York) tensor. The second part of the paper investigates Killing and conformal symmetry and also the nature of the zeros of the associated vector fields. The maximum dimension of the Killing and conformal algebras is calculated. A theorem regarding the reduction of the conformal algebra to a Killing algebra of a conformally related metric is given. (C) 1999 American Institute of Physics. [S0022-2488(99)01103-2].