= Oriented orthonormal frame bundle of anti-de Sitter spacetime
{title2=$SO(3,2)\longrightarrow\mathrm{AdS}_4$}
Represent the <Anti-de Sitter spacetime> quadric by $x\cdot x=-\ell^2$ in $\mathbb R^{3,2}$. Appending its timelike unit normal $x/\ell$ to an oriented tangent pseudo-orthonormal frame identifies the frame bundle with $SO(3,2)$. The stabilizer of that normal is $SO(3,1)$, so projection realizes $SO(3,2)/SO(3,1)$ as the base of a <principal bundle>. For the commonly used universal cover of the anti-de Sitter quadric, pull this bundle back along the covering map; the quadric itself has a periodic timelike coordinate.
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