Relativistic cosmologies with closed, locally homogeneous spatial sections

Abstract

The homogeneous Bianchi and Kantowski-Sachs metrics of relativistic cosmology are investigated through their correspondence with recent geometrical results of Thurston. These allow a partial classification of the topologies for closed, locally homogeneous spaces according to Thurston's eight geometric types. Besides, we learn which of the Bianchi-Kantowski-Sachs metrics can be imposed on closed spatial sections of cosmological models. This is seen as progress toward implementation of a postulate of the closure of space for both classical and quantum gravity. © 1985 The American Physical Society.