Actions with cohomogeneity zero or one on the de Sitter space dSn−1,1

The aim of this paper is to classify the connected Lie groups which act isometrically and with cohomogeneity c, where $c\in \{0,1\}$, on the de Sitter space $d{S}^{n-1,1}$ up to conjugacy in $SO(n,1)$ and then up to orbit equivalence. Among other results, we give the list of the groups represented in the isometry group of the de Sitter space $d{S}^{n-1,1}$.