Weingarten spacelike hypersurfaces in a de Sitter space

We study some Weingarten spacelike hypersurfaces in a de Sitter space S₁ⁿ⁺¹ (1). If the Weingarten spacelike hypersurfaces have two distinct principal curvatures, we obtain two classification theorems which give some characterization of the Riemannian product H^k(1−coth² ϱ)× S^n−k(1 − tanh² ϱ), 1 < k < n − 1 in S₁ⁿ⁺¹(1), the hyperbolic cylinder H¹(1 − coth² ϱ) × S^n-1(1 − tanh² ϱ) or spherical cylinder Hⁿ⁻¹(1 − coth² ϱ) × S¹(1 − tanh² ϱ) in S₁ⁿ⁺¹ (1)