- #1
Black Integra
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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]
[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]