Cohomogeneity One Three Dimensional Anti de Sitter Space, Proper and Nonproper Actions

In this paper we give a classification of closed and connected Lie groups, up to conjugacy in $Iso({\bf adS_3})$, acting by cohomogeneity one on the three dimensional anti de sitter space ${\bf adS_3}$. Then we determine causal characters of the orbits and the orbit spaces, up to homeomorphism, in both cases, proper and nonproper actions. When the action is proper, we show that there is no exceptional orbit and causal characters of the principal orbits are the same.