Is It Possible to Independently Vary Kij in Both Methods?

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I got the result that is consist with references in fisrt case. Is there anything wrong in 2nd way?
 
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Both are wrong. In the first case you are missing a 2 in both terms (still giving the same equation if you put the variation to zero). In the second case you missed a 2 only on the first term.
 
Thank you. I see.
Kij=gimgjnKmn
I should consider another Kij here.
 
Yes, you cannot vary Kij independently of Kij.
 

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