Extension of type-V and type-IX homogeneous cosmologies

Abstract

Homogeneous cosmologies described by four- parameter transitive groups of isometries G 4 with an additional dimension of four-m anifolds were obtained by extending Type-V and Type-IX cosmologies which involve isometry groups G 3 with transitive actions on three- manifolds. The group G 4 was specified via a translational symmetry over the extra dimension in order to extend a three-manifold metric which ad mits Bianchi Type-N (N=V, IX) to that of four-manifold. The extended metric of Types V and IX are solved explicitly.