Extension of Type-V and Type-IX Homogeneous Cosmologies

Homogeneous cosmologies described by four-parameter transitive groups of isometries G4 with an additional dimension of four-manifolds were obtained by extending Type-V and Type-IX cosmologies which involve isometry groups G3 with transitive actions on three-manifolds. The group G4 was specified via a translational symmetry over the extra dimension in order to extend a three-manifold metric which admits Bianchi Type-N (N=V, IX) to that of four-manifold. The extended metric of Types V and IX are solved explicitly.