Quotients of anti–de Sitter space

We study the quotients of $\mathrm{}(n+1\mathrm{})\mathrm{}$-dimensional anti–de Sitter space by one-parameter subgroups of its isometry group $\mathrm{SO}(2,n)\mathrm{}$ for general n. We classify the different quotients up to conjugation by $O(2,n).$ We find that the majority of the classes exist for all $n>~2.$ There are two special classes which appear in higher dimensions: one for $n>~3$ and one for $n>~4.$ The description of the quotient in the majority of cases is thus a simple generalization of the ${\mathrm{AdS}}_3$ quotients.