View source for Covariant differential

{{TEX|done}}
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|covariant derivative]] of the field $U$ along $X$. For detailed information, see [[Covariant differentiation|Covariant differentiation]].