Cohomogeneity one anti de Sitter space AdSn+1

Abstract

In this paper we study the anti de Sitter space AdSⁿ⁺¹ under a cohomogeneity one action of a connected closed Lie subgroup G of the isometry group. Among various results, for compact groups we determine the possible acting groups, the orbit space and principal and singular orbits. For noncompact groups it is shown that if there is a principal orbit which is either simply connected or totally umbilic, then there is only one orbit type. Furthermore, in the totally umbilic case, all orbits are congruent to AdSⁿ.