Springer Online Journal Archives 1860-2000
Abstract We consider an Einstein spaceV of the Petrov type II or III admitting a group of motionsG of high order. First we calculate the composition law and topological structure ofG. ThenV (or its submanifolds of transitivity) is represented as the homogeneous spaceG/H ofG,H being a subgroup ofG, and the actionG onV and the topology ofV are determined. The topologies of the spacesV are as follows: ℝ4 (spaceT*2), ℝ4 of ℝ3 T1 (spaceT 2), ℝ4 (spaceT*3), ℝ3 (submanifolds of transitivity in spaceT 3). In two cases (spacesT 2 andT 3) we have obtained metrics free of singularities.
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