Curvature of the two-dimensional hyperbolic polar metric
= Curvature of the two-dimensional hyperbolic polar metric
For the curvature convention
$$
R^\alpha{}_{\beta\gamma\delta}
=\partial_\gamma\Gamma^\alpha_{\beta\delta}
-\partial_\delta\Gamma^\alpha_{\beta\gamma}
+\Gamma^\mu_{\beta\delta}\Gamma^\alpha_{\mu\gamma}
-\Gamma^\mu_{\beta\gamma}\Gamma^\alpha_{\mu\delta},
$$
the independent nonzero mixed components are
$$
R^r{}_{\phi r\phi}=-\sinh^2r,
\qquad
R^\phi{}_{r\phi r}=-1,
$$
and the Ricci scalar is $R=-2/a^2$.