# Ordinary and covaraint derivative

1. Jan 4, 2012

### 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.

2. Jan 4, 2012

### 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.

3. Jan 4, 2012

4. Jan 4, 2012