On the regular space-like hypersurfaces in the de Sitter space \mathbb S^m+1₁ with parallel Blaschke tensors

2015/11/10 by Li, Xingxiao, Song, Hongru
#Differential Geometry (math.DG) #FOS: Mathematics #Primary 53A30 #Secondary 53B25

paper · doi:10.48550/arxiv.1511.02979

Abstract

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

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