Cohomogeneity one de Sitter space \(S^n_1\)
The paper belongs to the literature on non-transitive actions of the isometry groups of (pseudo-) Riemannian manifolds. A distinguished topic deals with ``cohomogeneity one'' (pseudo-) Riemannian manifolds, defined by an action with an orbit of codimension one and no orbit of codimension zero. Indeed, several results have been achieved in the literature for the Riemannian case. But, in the pseudo-Riemannian case, a difficulty arises from the fact that the action of closed Lie subgroups of the group of isometries does not need to be proper. In the present paper, the authors contribute to overcoming this difficulty. They study the distinguished case of a de Sitter space. Indeed, they study the actions in both proper and non-proper cases. In the first case, they characterise the acting groups and orbits and prove that the orbit space is homeomorphic to \(\mathbb R\). In the second case, they determine the groups and the orbits in some different cases and prove that the orbit space is not Hausdorff.
scientific article; zbMATH DE number 5808622
scientific article