Ordinary and covaraint derivative

[world line]

Hello
what is the meaning of covaraint derivative ?
where the ordinary derivative of a function whit respect to a variable is zero, it means that function doesn't depend on that variable.but what about covaraint derivative ?
for example the metric tensor may depends on coordinate but its covaraint derivative is zero.

 

[Markus Hanke]

The classical (directional) derivative is dependent on your choice of coordinates. The covariant derivative is not; is it covariant in the sense that it is defined in such a way as to be independent of its description in a particular coordinate system. That is why it is written as a directional derivative plus a term that compensates for any changes in coordinates, expressed through the Christoffel Symbols. It is basically a generalization of the classical derivative into Riemann geometry.

 

[Naty1]

what Hanke said, above...
more here: http://en.wikipedia.org/wiki/Covariant_derivative

 

[Naty1]

Just noticed this discussion: (did not read myself) maybe worth a look...

Covariant and Contravariant Tensors

https://www.physicsforums.com/showthread.php?t=507176