Formula_4587

\[\begin{gathered}d s^{2}=g_{11}\left(u^{1}, u^{2}\right)\left(d u^{1}\right)^{2}+2 g_{12}\left(u^{1}, u^{2}\right) d u^{1} d u^{2}+ \\+g_{22}\left(u^{1}, u^{2}\right)\left(d u^{2}\right)^{2}=g_{i k} d u^{i} d u^{k} .\end{gathered}\]