# Covariant derivative only for tensor

• A
Hi initially I am aware that christoffel symbols are not tensor so their covariant derivatives are meaningless, but my question is why do we have to use covariant derivative only with tensors? ?? Is there a logic of this situation? ???

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Tio Barnabe
I think there's more than one possible explanation. One of them is that by construction the covariant derivative measures the change of a vector in a given displacement. This is so by construction and by definition, i.e. we want to construct the derivative of a vector and we want to do so in analogy with case of funtions (construction), which is the limit of the difference of the vectors two points when the distance comes to zero, therefore it should be a vector too.

If you want to see the change of functions, you just use the ordinary derivative.

Orodruin
Staff Emeritus