Let \(F\) be a smooth tensor field . By analogy with the divergence formula for vector fields, we define the divergence of \(F\)
\begin{equation*} \div F = {\tr}_g(\nabla F), \end{equation*}where \({\tr}_g\) denotes the trace of covariant tensor fields . If \(F\) is purely contravariant there is no index to raise and therefore we consider the usual trace operator because the last index is an upper index already.