The Ricci Tensor comes from the Riemann Curvature Tensor:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]R^{\beta}_{\nu\rho\sigma} = \Gamma^{\beta}_{\nu\sigma,\rho} - \Gamma^{\beta}_{\nu\rho,\sigma} + \Gamma^{\alpha}_{\nu\sigma}\Gamma^{\beta}_{\alpha\ rho} - \Gamma^{\alpha}_{\nu\rho}\Gamma^{\beta}_{\alpha\sigma}[/tex]

The Ricci Tensor just contracts one of the indices:

[tex]R_{\nu\rho} = R^{\beta}_{\nu\rho\beta}[/tex]

What is the function of the Ricci Tensor and the Riemann Curvature Tensor? How does the contraction of indices change the effect?

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# Ricci Tensor

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