- #1

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i've had a couple of bashes and got nowhere other than to establish that its quotient theorem.

can i just pick a tensor of rank 3 to multiply it with or something?

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- Thread starter latentcorpse
- Start date

- #1

- 1,444

- 0

i've had a couple of bashes and got nowhere other than to establish that its quotient theorem.

can i just pick a tensor of rank 3 to multiply it with or something?

- #2

tiny-tim

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Prove that b_{ijkl}= ∫_{r<a}dV x_{i}x_{j}∂^{2}(1/r)/∂_{k}∂_{l}, where r=|x|, is a 4th rank tensor.

- #3

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yep.

- #4

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I have no idea how to solve this too, can you give me some idea please?

- #5

tiny-tim

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hi nhanle! welcome to pf!

ok, what is the test for something being a tensor?

- #6

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thank you for your reply. This is how vague the definition of tensor I am holding at the moment.

I am also confused about the Affine connection. Can you help me clarify this?

Thank you

- #7

tiny-tim

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i'm not going to type out a lecture on tensors and connections

please go back to your book or your lecture notes, and read up about tensors

- #8

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From my understanding, if one is to be a rank N-tensor, it should expect to have N derivative summations under coordinate transformation. Is that right?

- #9

tiny-tim

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if so, that should show you how to do it

- #10

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How to transform the partial derivatives? Thank you for being so patient with me

I also have question about the affine connection https://www.physicsforums.com/showthread.php?t=189456 which was raised long ago but no one seems to be interested in answering :(

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