Classification of spacelike conformal Einstein hypersurfaces in Lorentzian space Rⁿ⁺¹ 1

Let f: Mⁿ → Rⁿ⁺¹ 1 be an n-dimensional umbilic-free spacelike hypersurface in the (n + 1)-dimensional Lorentzian space Rⁿ⁺¹ 1 with an induced metric I. Let I I be the second fundamental form and H the mean curvature of f. One can define the conformal metric g =ⁿ n−1^{(∥I I∥2} − nH²)I on f (Mⁿ), which is invariant under the conformal transformation group of Rⁿ⁺¹ 1. If the Ricci curvature of g is constant, then the spacelike hypersurface f is called a conformal Einstein hypersurface. In this paper, we completely classify the n-dimensional spacelike conformal Einstein hypersurfaces up to a conformal transformation of Rⁿ⁺¹ 1.