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The Riemann Curvature Tensor is a tensor in Riemannian Geometry that describes the curvature of a manifold. Specifically, it measures the failure (known as the holonomy) of the ability of parallel transport to retain the direction of a vector in a space. In other words, it can be calculated as:


IdentitiesEdit this section

Correction to Proof of the Zeroth Bianchi Identity08:13

Correction to Proof of the Zeroth Bianchi Identity

More on Bianchi Identities14:57

More on Bianchi Identities

More on Bianchi Identities-014:57

More on Bianchi Identities-0

The definition of the Riemann Curvature Tensor immediately implies that:


And therefore;


Now, below are some other identities:

R_{\mu\nu(\rho\sigma)} = 0 See [1] .

First Bianchi Identity [2] .

Second Bianchi Identity [3] .

ReferencesEdit this section

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