Let g = {gij be a Riemannian metric on a manifold M of dimension n. It is Ricci curvature Rc(g) = {Rij} is given by the formula $$ {R_{{ij}}} = \frac{1}{{2(n - 1)}}{g^{{k2}}}\left[ {\frac{{{\partial ^{2}}}}{{\partial {x^{1}}\partial {x^{k}}}}{g_{{j2}}} + \frac{{{\partial ^{2}}}}{{\partial {x^{j}}\partial {x^{2}}}}{g_{{ik}}} - \frac{{{\partial ^{2}}}}{{\partial {x^{i}}\partial {x^{j}}}}{g_{{k2}}} - \frac{{{\partial ^{2}}}}{{\partial {x^{k}}\partial {x^{2}}}}gij} \right] + \frac{1}{{\left( {n - 1} \right)}}{g^{{k2}}}{g_{{pq}}}\left[ {r_{{ik}}^{p}r_{{j2}}^{q} - r_{{ij}}^{p}r_{{k2}}^{q}} \right] $$ $$ r_{{ij}}^{2} = \frac{1}{2}{g^{{k2}}}\left[ {\frac{\partial }{{\partial {x^{1}}}}{g_{{jk}}} + \frac{\partial }{{\partial {x^{J}}}}{g_{{ik}}} - \frac{\partial }{{\partial {x^{k}}}}{g_{{ij}}}} \right]. $$