= Poincare coordinates on anti-de Sitter spacetime
{c}
{title2=$ds^2=z^{-2}(dz^2+\eta_{ab}du^a du^b)$}
For Lorentzian boundary metric $\eta$ and $z>0$, this <Anti-de Sitter spacetime> patch has unit curvature radius. Its <orthonormal coframe> has connection $\omega^a{}_3=-\theta^a$ and curvature $\Omega^a{}_b=-\theta^a\wedge\theta_b$, giving <sectional curvature> $-1$. The full local <isometry> algebra is $\mathfrak{so}(d-1,2)$ in spacetime dimension $d$. A patch need not support every local Killing flow for all parameter values.
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