Abstract

The aim of this paper is to classify the cohomogeneity one conformal actions on the 3-dimensional Einstein universe Ein^{1,2}, up to orbit equivalence. In a recent paper, we studied the unique (up to conjugacy) irreducible action of PSL(2,R) on Ein^{1,2} and we showed that the action is of cohomogeneity one. In the present paper, we determine all the subgroups of Conf(Ein^{1,2}), up to conjugacy, acting reducibly and with cohomogeneity one on Ein^{1,2}. We show that any cohomogeneity one reducible action on Ein^{1,2} induces a fixed point in the 4-dimensional projective space RP^4. Also, we describe all the codimension one induced orbits by these actions.