Riemann's curvature tensor help!

Main Question or Discussion Point

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]
 

Answers and Replies

1,444
4
You need also the definition of the Riemann curvature tensor.
 

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