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A Contraction between Levi-Civita symbol and Riemann tensor

  1. Dec 22, 2016 #1
    How to proof that
    εμνρσ Rμνρσ =0 ?

    Thanks.
     
  2. jcsd
  3. Dec 22, 2016 #2

    ShayanJ

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    Gold Member

    Last edited by a moderator: Dec 22, 2016
  4. Dec 22, 2016 #3
    I'm not sure Rμνρσ = Rμ(νρ)σ or not? If so, the problem solved for me.

    Thanks.
     
  5. Dec 22, 2016 #4

    ShayanJ

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    Gold Member

    I thought those symmetries would help, but it seems they don't. Start with the first Bianchi identity and contract all the indices with a Levi-Civita symbol. Rearranging the indices of the Levi-Civita symbol in two of the terms will give you what you want.
     
  6. Dec 22, 2016 #5
    OK, I know use the Bianchi identity
    Rμ[νρσ]=0
    Thanks!
    ShayanJ!!
     
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