De Sitter spacetimes with torsion in the model of dS gauge theory of gravity

In the model of de Sitter gauge theory of gravity, the empty homogenous and isotropic spacetimes with constant curvature scalar and nonvanishing homogenous and isotropic torsion must have de Sitter metrics. The static de Sitter spacetime with static, O(3)-symmetric, vector torsion is the only spherically symmetric, vacuum solution with the metric of the form $g_{\mu\nu}={\rm diag}(A^2(r),-B^2(r),-r^2,-r^2\sin^2\th)$. The expressions of the torsion for different de Sitter spacetimes are presented. They are different from one to another. The properties of different de Sitter spacetimes with torsion are also studied.