# Covariant differential

A generalization of the notion of a differential to fields of different geometric objects. It is a tensor $1$-form $DU$ on a manifold with values in the module of tensor fields $U$ defined by the formula
$$(DU)(X)=\nabla_XU,$$
where $\nabla_XU$ is the covariant derivative of the field $U$ along $X$. For detailed information, see Covariant differentiation.