Kantowski Sachs metric

In general relativity the Kantowski-Sachs metric describes a homogeneous but anisotropic universe whose spatial section has the topology of R × S 2 . The metric is:

The isometry group of this spacetime is R × S O ( 3 ) . Remarkably, the isometry group does not act simply transitively on spacetime, nor does it possess a subgroup with simple transitive action.