Recent content by Vyrkk

And now I understand why this requirement is needed, despite Caroll not stating its use anywhere in the derivation. Thank you!

Mmh finally we're getting somewhere. So if I take the covariant derivative of a tensor product of a one-form and a vector, I can develop using the Leibniz product rule for the tensor product. Taking the contraction on each side, I get my result. But under one condition: the contraction has to...

Well, the product rule given p. 55 as part of the definition is a product rule for tensor product, not for a one form acting on a vector field or for two vector fields

It's not that I think it's not defined, it's that I haven't seen it defined anywhere. As far as I know, the covariant derivative has a Leibniz rule for a scalar field times a vector field, and for the tensor product of any two tensors. I am using my professor's Lecture notes and complement...

I am trying to derive the expression in components for the covariant derivative of a covector (a 1-form), i.e the Connection symbols for covectors. What people usually do is take the covariant derivative of the covector acting on a vector, the result being a scalar Invoke a product rule to...