K=\frac{1}{g_{11}g_{22}-g_{12}^2}\left(\sum_{k,l=1}^{2}(\Gamma_{12}^{k}\Gamma_{12}^{l}-\Gamma_{11}^{k}\Gamma_{22}^{l})g_{kl}+\frac{\partial^2 g_{12}}{\partial u_1 \partial u_2} - \frac{1}{2}\frac{\partial^2 g_{11}}{\partial u_2 \partial u_2} - \frac{1}{2} \frac{\partial^2 g_{22}}{\partial u_1 \partial u_1}\right)