# Riemann's curvature tensor help!

1. Feb 19, 2012

### Black Integra

Please, anyone tell me how to proof this equation:

${R^\rho}_{\sigma\mu\nu} = \partial_\mu\Gamma^\rho_{\nu\sigma} - \partial_\nu\Gamma^\rho_{\mu\sigma} + \Gamma^\rho_{\mu\lambda}\Gamma^\lambda_{\nu\sigma} - \Gamma^\rho_{\nu\lambda}\Gamma^\lambda_{\mu\sigma}$

Given a definition of parallel transport here :

$dV^{m}=-\Gamma^{m}_{np}V^{n}dx^{p}$

2. Feb 20, 2012