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Riemann's curvature tensor help!

  1. Feb 19, 2012 #1
    Please, anyone tell me how to proof this equation:

    [itex]{R^\rho}_{\sigma\mu\nu} = \partial_\mu\Gamma^\rho_{\nu\sigma}
    - \partial_\nu\Gamma^\rho_{\mu\sigma}
    + \Gamma^\rho_{\mu\lambda}\Gamma^\lambda_{\nu\sigma}
    - \Gamma^\rho_{\nu\lambda}\Gamma^\lambda_{\mu\sigma}[/itex]

    Given a definition of parallel transport here :

    [itex]dV^{m}=-\Gamma^{m}_{np}V^{n}dx^{p}[/itex]
     
  2. jcsd
  3. Feb 20, 2012 #2
    You need also the definition of the Riemann curvature tensor.
     
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