  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.
