- #1
Mr-R
- 123
- 23
Dear All,
I am teaching myself tensors for the first time. I am using D'Inverno's book and got stuck at page 73. Basically, he says: demand that the first term on the left of the equation to be a type (1,1) tensor. Then he gets the affine connection transformation.
I basically wrote the first term as a second rank mixed tensor transformation. Then I got stuck. I am not sure on how to isolate (?) the affine connection and show how it transforms. I tried many times but failed due to my lack of knowledge of tensors. Could someone help me understand this please?
[itex]\nabla_{c}X^{a}[/itex]= [itex]\partial_{c}[/itex][itex]X^{a}[/itex]+[itex]\Gamma_{bc}^{a}[/itex][itex]X^{b}[/itex]
Thanks in advance! (Sorry if my post isn't very informative as I have to go for 6 hours. When I come back I will be more than happy to upload pictures of my attempts)
I am teaching myself tensors for the first time. I am using D'Inverno's book and got stuck at page 73. Basically, he says: demand that the first term on the left of the equation to be a type (1,1) tensor. Then he gets the affine connection transformation.
I basically wrote the first term as a second rank mixed tensor transformation. Then I got stuck. I am not sure on how to isolate (?) the affine connection and show how it transforms. I tried many times but failed due to my lack of knowledge of tensors. Could someone help me understand this please?
[itex]\nabla_{c}X^{a}[/itex]= [itex]\partial_{c}[/itex][itex]X^{a}[/itex]+[itex]\Gamma_{bc}^{a}[/itex][itex]X^{b}[/itex]
Thanks in advance! (Sorry if my post isn't very informative as I have to go for 6 hours. When I come back I will be more than happy to upload pictures of my attempts)
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