Covariant Derivative: Proving Rank-2 Tensor Components

Join the discussion
Ask a follow-up here, or get your own question answered by working scientists, mathematicians and engineers — people, not an autocomplete.
Real named experts · corrections over time · the nuance an AI answer skips
3 replies · 4K views
ehrenfest
Messages
2,001
Reaction score
1

Homework Statement


I am trying to show that the components of the covariant derivative [tex]\del_b v^a are the mixed components of a rank-2 tensor.<br /> <br /> If I scan in my calculations, will someone have a look at them?<br /> <br /> <br /> <br /> <h2>Homework Equations</h2><br /> <br /> <br /> <br /> <h2>The Attempt at a Solution</h2>[/tex]
 
Physics news on Phys.org
pretty pretty please
 
Here are my calculations. It took me forever to scan them and put them in a file small enough to upload. :(

Anyway. The "stuff" is the correct transformation for a mixed second rank tensor which means the other term (the one that I wrote out) needs to vanish. The problem is that I do not see why it vanishes. Does anyone else?

By the way--can other people not click on the attachment and see it under it gets approval?
 

Attachments

  • covariant derivative 1.jpg
    covariant derivative 1.jpg
    21.5 KB · Views: 600
Last edited: