- Thread starter McGravity
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Yes there is " partial covariant derivative".I understand covariant derivatives which are given in many textbooks, but is there such a thing as a partial covariant derivative, that is the covariant derivative(s) of Z as a function of x and y?

Type in those terms in Google and you'll be referred to >1740 sites!

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I thought that the covariant derivative for the case of a scalar function coincides with the gradient of it, and when you generalize it to include vectors and tensors you get also the connection coefficients. Am I wrong?That is a definition but I was hoping for an explanation, which isn't quite the same thing. If I can find how to covariantly differentiate V = r Cos theta that would be a great help.

Yes that sounds right but it's just what you would find in any textbook. My problem came from Relativity Demystified (ironic title)I thought that the covariant derivative for the case of a scalar function coincides with the gradient of it, and when you generalize it to include vectors and tensors you get also the connection coefficients. Am I wrong?

No that's way above my head. I am a physicist/engineer, not a mathematicianView attachment 20674View attachment 20675View attachment 20676

I hope this will help you a bit more.

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Indeed it is heavy stuff, but standard differential geometry for GR.No that's way above my head. I am a physicist/engineer, not a mathematician

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