Blaschke Isoparametric Hypersurfaces in the Conformal Space ${\mathbb{Q}}_1^{n+1}$}, II

Let $x:\mathbf{M}\to {\mathbb{Q}}_1^{n+1}$ be a regular space-like hypersurface in the conformal space ${\mathbb{Q}}_1^{n+1}$. We classify all those hypersurfaces with parallel Blaschke tensor in the conformal space up to the conformal equivalence.