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## Main Question or Discussion Point

Hi. I am attempting to gain some intuition for what the covariant derivative of a tensor field is.

I have a good intuition about the covariant derivative of vector fields (measuring how the vector changes as you move in a particular direction), and I understand how to extend the covariant derivative to tensors with the leibnitz product rule. I can calculate the tensor covariant derivative and prove things about it, but I still don't understand what it *is*.

Anyone?

I have a good intuition about the covariant derivative of vector fields (measuring how the vector changes as you move in a particular direction), and I understand how to extend the covariant derivative to tensors with the leibnitz product rule. I can calculate the tensor covariant derivative and prove things about it, but I still don't understand what it *is*.

Anyone?