Spatially homothetic cosmological models

Spatially homothetic cosmological models are defined as space-time manifolds acted on by a 3-parameter group of transformations transitive over spacelike hypersurfaces, whose effect is to multiply the metric by a constant conformal factor. Previous work on these models is reviewed briefly and the algebraic classification scheme of Eardley is described. Explicit forms of the metric and group generators are given for each class in terms of a conformally synchronous coordinate system using an invariant orthogonal basis of 1-forms. It is shown that certain subclasses are necessarily incomplete in the sense that a singularity of the conformally synchronous system must develop within a finite time.This article is Dedicated to Achille Papapetrou on the occasion of his retirement and forms a part of the Papapetrou Festschrift.