On the regular space-like hypersurfaces in the de Sitter space ${\mathbb{S}}_1^{m+1}$ with parallel Blaschke tensors

Abstract

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

submitted