Spacelike hypersurfaces with constant conformal sectional curvature in ℝ₁ⁿ⁺¹

Let f:Mⁿ → ℝ₁ⁿ⁺¹ 1 be an n-dimensional umbilic-free spacelike hypersurface in the (n+1)-dimensional Lorentzian space ℝ₁ⁿ⁺¹ 1 . One can define the conformal metric g on f which is invariant under the conformal transformation group of ℝ₁ⁿ⁺¹ . We classify the n-dimensional spacelike hypersurfaces with constant sectional curvature with respect to the conformal metric g when n ≥ 3. Such spacelike hypersurfaces are obtained by the standard construction of cylinders, cones or hypersurfaces of revolution over certain spirals in the 2-dimensional Lorentzian space forms S ₁ ²;ℝ₁²; ℝ₁₊², respectively.