# Covariant differential

From Encyclopedia of Mathematics

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.

**How to Cite This Entry:**

Covariant differential.

*Encyclopedia of Mathematics.*URL: http://www.encyclopediaofmath.org/index.php?title=Covariant_differential&oldid=32829

This article was adapted from an original article by I.Kh. Sabitov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article