On the regular space-like hypersurfaces in the de Sitter space Sᵐ⁺¹₁ with parallel Blaschke tensors

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In this paper, we use two conformal non-homogeneous coordinate systems, modeled on the de Sitter space Sᵐ⁺¹₁, to cover the conformal space Qᵐ⁺¹₁, so that the conformal geometry of regular space-like hypersurfaces in Qᵐ⁺¹₁ is treated as that of hypersurfaces in Sᵐ⁺¹₁. As a result, we give a complete classification of the regular space-like hypersurfaces (represented in the de Sitter space Sᵐ⁺¹₁) with parallel Blaschke tensors.