Is it true, that Ricci curvature of the $n$-ball is equal to zero? I have calculated it with use of formula $$ R_{\alpha \beta}=R^{\rho}_{\alpha \rho \beta}=\partial_{\rho} \Gamma^{\rho}_{\beta \alpha}-\partial_{\beta} \Gamma^{\rho}_{\rho \alpha}+\Gamma^{\rho}_{\rho \lambda} \Gamma^{\lambda}_{\beta \alpha}-\Gamma^{\rho}_{\beta \lambda} \Gamma^{\lambda}_{\rho \alpha} $$
The metric is a standard metric on the ball.