Cohomogeneity one anti de Sitter space \(H^3_1\)
In this paper the authors study the manifold \(H^3_1\) under the action of a closed Lie subgroup of isometries \(G \subseteq Iso(H^3_1)\) with an orbit of dimension two. It is proved that if \(H_1^3\) is of cohomogeneity one under the proper action of a connected closed Lie group \(G\) of isometries then there exists no space like orbit. The authors determine the acting groups up to conjugacy, \(G\subset SL(2, \mathbb R)\times SL(2,\mathbb R)\). They find the orbits up to isometry and finally they characterize the space \(H^3_1/G\). The results are exposed in several theorems which consider either the existence of a degenerate orbit or the non existence of a degenerate nor a singular orbit.
scientific article; zbMATH DE number 5604228