View source for 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

<table class="eq" style="width:100%;"> <tr><td valign="top" style="width:94%;text-align:center;"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c026/c026860/c0268604.png" /></td> </tr></table>

where <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c026/c026860/c0268605.png" /> is the [[Covariant derivative|covariant derivative]] of the field <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c026/c026860/c0268606.png" /> along <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/c/c026/c026860/c0268607.png" />. For detailed information, see [[Covariant differentiation|Covariant differentiation]].