Formula_4593

\[\begin{gathered}R_{i j k l}=\frac{1}{2}\left(\frac{\partial^{2} g_{i k}}{\partial x^{j} \partial x^{l}}+\frac{\partial^{2} g_{j l}}{\partial x^{i} \partial x^{k}}-\frac{\partial^{2} g_{i l}}{\partial x^{j} \partial x^{k}}-\frac{\partial^{2} g_{j k}}{\partial x^{j} \partial x^{k}}\right)- \\-g_{r s}\left(\Gamma_{j k}^{r} \Gamma_{i l}^{s}-\Gamma_{j l}^{r} \Gamma_{i k}^{s}\right) .\end{gathered}\]