# Difference between revisions of "Covariant differential"

From Encyclopedia of Mathematics

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− | A generalization of the notion of a differential to fields of different geometric objects. It is a tensor | + | {{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 | + | where $\nabla_XU$ is the [[Covariant derivative|covariant derivative]] of the field $U$ along $X$. For detailed information, see [[Covariant differentiation|Covariant differentiation]]. |

## Latest revision as of 15:33, 10 August 2014

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://encyclopediaofmath.org/index.php?title=Covariant_differential&oldid=18963

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