ON NON-PROPER ACTIONS ON THE DE SITTER SPACE Sn

In this paper after giving a short introduction to the subject ”G-manifolds”, we concentrate on the isometric action of a closed noncompact Lie subgroup G ½ Iso(Sn 1 ) on the de Sitter space Sn 1 . When the action is not proper and there is an orbit of codimension one, we give a suitable definition for principal and singular orbits and determine the group G and consequently the orbits in some different cases and prove that the orbit space is not Hausdorff