Equation 15.18.4040CD1B311623

\begin{equation} \operatorname {Ric}^{(2)}_{l\bar k} =\operatorname {Ric}^{(1)}_{l\bar k} -g^{i\bar j}\bigl ( \nabla _ l\overline C_{\bar j\bar k i} +\nabla _{\bar j}C_{il\bar k} \bigr ). \end{equation}