Extending Bianchi's classification of homogeneous three-manifolds - Abdullah, Aslam (LAP LAMBERT Academic Publishing, 2016)
A few of the Bianchi types of homogeneous cosmologies described by three-dimensional groups of motions G(3) with transitive actions on three- manifolds were extended to those involving transitive groups of motions G(r) 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 G(r) was chosen.