Extending Bianchi’s Classification of Homogeneous Three-Manifolds - Abdullah, Aslam (2006)
A few of the Bianchi types of homogeneous cosmologies described by threedimensional groups of motions 3 G with transitive actions on three-manifolds were extended to those involving transitive groups of motions r G with additional dimensions of four-manifolds. In order to extend a three-manifold metric which admits the Bianchi type N (N=I, II, V, IX) to that of four-manifold, the group r G was chosen.