# Difference between revisions of "Covariant differential"

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A generalization of the notion of a differential to fields of different geometric objects. It is a tensor <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c026/c026860/c0268601.png" />-form <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c026/c026860/c0268602.png" /> on a manifold with values in the module of tensor fields <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c026/c026860/c0268603.png" /> defined by the formula | A generalization of the notion of a differential to fields of different geometric objects. It is a tensor <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c026/c026860/c0268601.png" />-form <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c026/c026860/c0268602.png" /> on a manifold with values in the module of tensor fields <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c026/c026860/c0268603.png" /> defined by the formula | ||

## Revision as of 15:32, 10 August 2014

A generalization of the notion of a differential to fields of different geometric objects. It is a tensor -form on a manifold with values in the module of tensor fields defined by the formula

where is the covariant derivative of the field along . 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