In this paper, we use two conformal non-homogeneous coordinate systems, modeled on the de Sitter space ${ \mathbb S}^{ m+1}_1$, to cover the conformal space ${ \mathbb Q}^{ m+1}_1$, so that the conformal geometry of regular space-like hypersurfaces in $\mathbb{ Q}^{ m+1}_1$ is treated as that of hypersurfaces in ${ \mathbb S}^{ m+1}_1$. As a result, we give a complete classification of the regular space-like hypersurfaces (represented in the de Sitter space ${ \mathbb S}^{ m+1}_1$) with parallel Blaschke tensors.
Categories: math.DG